So without further ado here's the list of games worth playing from each genre, a list of which has been lifted directly from Wikipedia.
Ball and Paddle: Wizorb
A sadly overlooked indie gem in the vein of classics such as Arkanoid. You play a wizard who has an orb and your wand is a paddle. You pop monsters and treasure chests and various other stuff throughout a neat little adventure to build a town.
Beat Em Up: Guilty Gear Isuka
Guilty Gear has a rather high skill ceiling but it's also a one on one fighter that's easy to pick up and play. From button mashing to actual skill based fighting Guilty Gear provides a beautiful flashy fighter that'll work on most machines at a minimal cash outlay. Alternately, Guilty Gear XX is also an excellent choice and both are available on GOG.com for the kind of cash you've got down the back of your sofa cushions.
Hack & Slash: Metal Gear Rising Revengance
A spin off from the Metal Gear Solid series where you play as Raiden, cyborg ninja extraordinaire as he hacks and slashes his way through the near future where there's robot cat things, robot helicopters, robot spheres with arms and a whole host of Metal Gear style crazy bosses. The gameplay is slick and easy to pick up and Zandatsu (Cut and Take) mode is so satisfying.
Mascot Fighter: Super Smash Bros. Brawl
Smash Bros has been the reigning king of mascot fighters since the N64 days and the incremental improvements Nintendo manages to crowbar in as well as the growing roster of characters and powerups manages to keep the series fresh for newcomers and old fans each entry. It has some competition now from Playstation All Stars but Smash Bros is by far the superior game.
Often overlooked for its titanic overhead cousins, League Of Legends and DOTA 2. Smite deserves a fair amount of recognition for its well thought out translations of real world deities and stand-out community. It's rare to get a hostile team in Smite and newbies have enough options to play against bots both alone and with other players to hone their skills.
Maze Game: Pac Man
Skip the Atari 2600 version and many of the later iterations like Ms. Pac Man and Pac Man Jr. and go right for the classic arcade version.
Pinball: Pinball FX2
This was a tough choice between Pinball FX2 and Naxat's Crush games (Devil's Crush and Jaki Crush) on the PC Engine. Pinball FX2 wins out on two counts; it's easier to get your hands on these days without laying out hundreds of pounds and it has the advantage of shiny modern graphics and physics systems. That said, if you're in a position to get a hold of Devil's or Jaki Crush, do so.
2D Platformer: Shovel Knight
Barely edging out Super Mario World as the best platformer to recommend, Shovel Knight is the epitome of years of experience all mashed together and brought to perfection. It manages to be both an homage to old games while being something fresh and unique all of its own. See the review for why you should play it.
3D Platformer: Jumping Flash
Quite possibly the only first person robot rabbit themed platformer with firework named power-ups on the Playstation. For a game of this era it has aged spectacularly well whereas other games have either aged poorly due to graphical limitations or older gaming conventions, Jumping Flash is so out there as to be almost immortal on both fronts. Or you can play Mario 64 for the hundredth time.
First Person Shooter: Metroid Prime
In a market oversaturated with FPS games it's hard to choose one that isn't one of the absolute classics like Doom or Unreal Tournament '99. Metroid Prime however stands out as a game which did FPS right on consoles, twice. Both the original Gamecube and revamped (and superior) Wii version provide a compelling story, believable world and all the staples of the Metroid series plus a few new twists and mechanics. You're doing yourself a disservice if you've not played at least the first Prime game.
Massively Multiplayer Online First Person Shooter: Planetside 2
With a newly added fourth continent and a wealth of terrain, classes, weapons, vehicles and a community full of varying degrees of seriousness it's hard not to find something to like amongst the three factions and gigantic amount of content. It helps that it's free with optional transactions/subscription too so there's nothing to lose by giving it a look.
Light Gun Shooter: House Of The Dead Overkill
Positively drowning in vulgar humour and throwing around enough swear words to make anyone feel uncomfortable. It's a glorious throwback to the grindhouse of yore that has appeared best on Wii and PC, with the PC having the lovely addition of a Typing Of The Dead mode in addition to the light gun style mode. Nothing like killing zombies with typing.
Shoot Em Up: Tyrian 2000
There have been many many quality shoot em ups over the years, names like Raiden and Ikaruga stand out especially and perhaps Lords Of Thunder holds the undisputed crown as king of shooters but it's incredibly difficult to get a hold of without a hefty parting of cash. Tyrian 2000 is the finest version of Tyrian ever released (and it's free on GOG.com) with the campaign, arcade mode, all the neat little secrets and cheats intact and the ease of use that comes with the preconfigured DOSBOX install.
Tactical Shooter: Rainbow Six 3: Raven Shield
Plotting the timing and tactics an entire squad of special operatives are going to use in any one of a few dozen super tense, realistic (for the time, and still not half bad these days) scenarios and then executing those plans either flawlessly, or more commonly, in as much of a clownshoes fashion as possible is an enjoyable way to spend an afternoon either on your own or with mates. Swat 4 captures a good chunk of what makes Rainbow Six 3 a great game in a more accessible package too, so there's a bit of variety in choosing which man-shooty-tactical setting you prefer.
Third Person Shooter: Spec Ops: The Line
Often overlooked as a cookie cutter third person shooter about a bunch of gritty blokes in the grit filled gritty ruins of Dubai doing gritty things with grit while eating grits. Spec Ops is a re-telling of the Heart Of Darkness tale that has a surprising emotional impact on the player and even manages to pull the player into the role of the lead character via some nifty meta scripting. Or you can just enjoy the slow-mo headshots and killing people with sand, but then you'd be missing out on feeling like a terrible human being.
Action Adventure: Tomb Raider (2013)
The newest Tomb Raider sees Lara rebooted to a younger version and takes us along on the ride as she explores the mythical island of Yamatai with her mostly likable companions. It's got a bit of sneaking, a bit of shooting and plenty of platforming but it's never too difficult in any one aspect to become frustrating. A mix of some fantastical creatures and settings is only slightly marred by the poor quick time events and the fact that if Laras hair tech glitches it looks like she has a bum hole on the back of her head.
Survival Horror: Resident Evil 4
Resi 4 may be a bit of a cliche pick but it's right at the peak of the survival horror genre. Not only is it a direct continuation of the grandaddy of survival horror games but it has one of the best, genuinely creepy settings and manages to mix in the action and survival aspects perfectly. Even when you're sitting on a stack of good ammo and the shotgun that put Ol Yeller down you still feel like a frightened blonde girlyboy rabbit lost in the nondescript European backwoods. Yes, I called Leon a girlyboy but I still love him.
Text Adventure: Fish!
Magnetic Scrolls masterpiece about an interdimensional secret agent that's taking a vacation as a fish. It comes with nifty colour images along with the glorious writing and a text parser that just might surprise you from time to time. It may not be as easy to get a hold of as Zork but the Amiga version of Fish! is a game every text adventure aficionado should attempt to seek out. Or if you're lazy just play Zork on PC, you can even get it for free legally with a bit of googling.
Point & Click Adventure: The Walking Dead (both seasons)
While not a traditional point and click adventure The Walking Dead series is the evolution of those classics such as Monkey Island and Full Throttle. Telltale took out all the bollocks bits like obtuse puzzles and unwinnable scenarios (seriously Sierra...) and streamlined the gameplay to make you feel like you're a part of the cast. The Wolf Among Us is in the same style and is also well worth a look.
Visual Novel: Long Live The Queen
A mixture of Japanese style visual novel and statistic building role playing game, Long Live The Queen manages to make a typically passive genre into a multi-threaded tangle of conspiracy, deceit, assassination attempts and fatal accidents that George R R Martin can only have sad little wet dreams about. Plus you're a pretty pretty princess so there's every little boy's dream come true right there.
Western style or Computer Role Playing Games: Elder Scrolls 3: Morrowind
Mudcrabs, prisoners, silt striders, werewolves and vampires! Oh my! Not the graphically slickest of the Elder Scrolls series but it features one of the best role playing setups and a unique conversation system where you can actually type in keywords to ask people about makes Morrowind a very enjoyable place to explore. I'd love to recommend Ultima 4 and onwards too, but they're positively offensive to modern gaming sensibilities.
Japanese Role Playing Games: Bravely Default
The culmination of humanity's JRPG knowledge over the past three decades. It has charm, challenge, character(s) and the titular Brave and Default system to bring a new twist to turn based battling. It even has a town building mechanic tied to the story of the game that helps you get invested in everything that's going off as it all feeds back into each other. There's also a bloke called Ringabel, and that's funny.
Sandbox Role Playing Games: Ultima Worlds Of Adventure 2: Martian Dreams
You get to bugger about with some of history's most famous figures, who may or may not be represented accurately but you end up going to Mars to have a grand old adventure. Sure the interface is a bit clunky and the gameplay may not have aged as graciously as a fine wine but it's an adventure that's worth putting the effort in. If you can't be arsed with that, go play Skyrim you pleb.
Action Role Playing Game: Deus Ex Human Revolution
I'm sure I'll get a lot of shit for not naming the original Deus Ex here but I highly urge you to go play that too, perhaps even play it first. However, Human Revolution is a worthy successor to the Deus Ex name and has the same globe hopping story of intrigue and plot twists that made the original so much fun. Plus we get to see where Tracer Tong got his name from so if you need further justification for playing Human Revolution first, it's the chronologically right thing to do.
Massively Multiplayer Online Role Playing Games: Guild Wars 2
Taking away a lot of the typical skill rotation boredom in favour of actually hitting a dodge button and flipping out of the way and introducing a novel new way to get your questing fix on. Guild Wars 2 also features the pay once play forever model so there's no subscription fee to worry about either, oh and you get to play a four eared cat, wolf person and meet Rytlock Brimstone which just may be the most metal name of any MMO character ever.
Roguelikes: Dungeons Of Dredmor
The original Rogue will always hold a special place in the hearts of gamers of a certain age but the resurgence of popularity the Roguelike genre is seeing has spawned dozens of fantastic takes on the old formula. Rising to the top of the bubbling roguelike vat is Dungeons Of Dredmor and its two expansions and glut of excellent mods. Mixing humour with deep strategy and the traditional turn based incomprehensible stat whoring Dungeons Of Dredmor has it all in spades and the neat graphical presentation means that it's more welcoming to new roguelike players than the complicated looking character sheet makes out.
Tactical Role Playing Games: Divinity: Original Sin
Divinity beats out the likes of Wasteland 2 only because it's actually seen a proper release already. It has excellent characters, a rich and complex lore that's a pleasure to delve into and a quirky, expansive world that you'll want to explore every inch of. Divinity is also a proper role playing game too, harkening back to the older days of Ultima 7 with in depth interactions and conversations, complex relationships and an Imp called Zixzax. Any fan of role playing games should absolutely search this one out and bring a friend along for excellently implemented cooperative play too.
Construction and Management Simulation: Dungeon Village
This android and iOS game may not have the fancy doohickeys of Sim City or Sid Meiers Railroads but it brings plenty of charm to the table. In it you build up a fantasy themed village, attract and house adventurers and hold events to boost their stats while balancing out giving gifts of better gear with the need for them to buy stuff so you can build more stuff. It'll cost a couple of quid but it's well worth the investment and many many other Kairosoft games on android and iOS are worth picking up too, I'd recommend Epic Space Story or Ninja Village as alternatives.
Life Simulation: Tamagotchi
A craze of the mid nineties, these little hand-held devices had a little LED screen and a few buttons with which to nurture and raise a nondescript little creature into a grand and majestic beast. All the fun of a real pet without the commitment, but you still have to pick up the poo. Though 20 years old, these things are still pretty easy to pick up from sites like ebay and their enduring popularity in some countries means there's more than ever to choose from, though I'd recommend the classics. Alternatively, Viva Pinata is another excellent twist on the genre.
Flight Simulation: DCS A-10C
The Warthog, a big ugly beast of a plane that eats tanks and AAA for breakfast. It'll fly on one engine with half a wing and the pilot sits in the affectionately named titanium bathtub. Working equally well with a keyboard and mouse or full HOTAS setup it's pretty much impossible to find a more dedicated or accurate flight simulator, with simulated computer systems and a fully clickable cockpit and comprehensive tutorials you too can learn how to turn on a multi-million dollar warplane and blow up pretend tanks and stuff with a pretend jet firing pretend bullets from a pretend gun bigger than a Volkswagen Beetle. RAAAAAAARP!
Driving Simulation: Forza 5
While it's lacking some aspects like weather and the ability to punch Jeremy Clarkson in his stupid face Forza 5 is still the peak of the series. It's just as exhilarating to nip around Laguna Seca in a Mini Cooper as it is a Bugatti Veyron and with every car having an interior view and high resolution model and textures it puts Gran Turismo very firmly out to pasture. Drivatars learn from your driving and behave accordingly in other people's games, not just earning you money but providing the feel of every race being a real race with real drivers, just without the constant barrage of nonsensical racism you usually get from playing online.
4X Strategy: Civilization 5
Managing an entire civilization from the ancient era to future times sounds like a daunting task but Civ 5 manages to make it as easy or hard as you want. A couple of excellent expansion packs and a handful of quality DLC bit later and you have a very robust strategy that mixes diplomacy, exploration, research and war to the most finely honed blend of the entire genre. There's also an excellent modding community with custom leaders/civilizations, scenarios and the like. I'd highly recommend the Faerun Scenario, which is a total conversion where players get to manage one of the dozens of Forgotten Realms countries. Alternatively, Age Of Wonders 3 provides a more combat focused take on the 4x genre with an awesome fantasy spin.
Artillery Strategy: Worms Revolution
The latest in the long running Worms series by Team 17, Revolution brings the series back to the Armageddon glory days with beautiful 2d arenas, quirky humour and more concrete donkeys than you can shake an annelid at. Bring a mate or three for an absolute blast.
Real Time Strategy: Syndicate (no, not that one, the good one by Bullfrog)
Make no mistake, Syndicate is an RTS through and through. It might not have base building but those four trenchcoat wearing, persuadertron wielding badasses under your command will feel like family if they ever survive a mission. With a polygonal sequel (Syndicate Wars) and an upcoming spiritual successor (Satellite Reign) the original still manages to hold up as a unique and engrossing cyberpunk strategy romp. Don't forget your bionic eyes though because it's either going to be a small window or looking like a waffle puked on your monitor, long live low res!
Massively Multiplayer Real Time Strategy: Age Of Empires Online
In a niche genre plagued by wallet gouging tactics, Age Of Empires Online stands out as an evolution of the classic strategy staple while being a fair approximation of an MMORTS that doesn't force the PvP on players. It has a generous series of single player and coop campaigns, skirmish modes and a city building meta game. As a caveat to this entry, the servers will be shut off soon so don't invest any money in it if you give it a look, however Airmech and the upcoming Homeworld/Hardware Shipbreakers are worthy alternatives.
Real Time Tactics: Total War: Shogun 2
Feudal Japan, check. Foreign sounding names, check. Sweet battle scenes, check. Managing your clan to dominance through the land of the rising sun, check. Shogun 2 presents a very cohesive experience for the armchair general and the Japanese names for units and formations means you learn their purposes and quirks more than you might if they were just called 'spearman' or 'swordsman'.The introduction of gunpowder and other weapons also changes up the strategy part way through to keep players on their toes.
Tower Defense: Anomaly 2
As a twist on tower defense, Anomaly is a tower offence game in which you must escort a convoy of vehicles through arenas filled with various turrets using 4 basic abilities and the ability to pause and swap your convoys route at intersections to either complete optional objectives or take the path of least resistance. Upgradable and transformable vehicles in the convoy also add some much needed strategy and the occasional hectic rush to save a badly damaged unit. There's even a multiplayer mode where a defender places towers and an attacker tries to break through.
Turn Based Strategy: Front Mission 3
A lengthy story, likable characters and some of the most memorable mech punching to ever come out of a video game. Every turn of combat is a nail biting thriller as the attack animations play out and you hold your breath for the damage numbers or miss notification. Made by Square Enix, Front Mission 3 has the familiar turn based combat infused with a grid based tactics and rather deep mech customization. On a personal level, Front Mission 3 is easily on par with Final Fantasy 7 for the title of greatest PS1 era RPG.
Turn Based Tactics: Chaos (can be played online here)
You're given a wizard and a handful of randomly selected spells and told to go kick ass against 1, 2 or 3 opponents on a plain black background. You'll find yourself loving those 6 green pixels you're told is a gooey blob and cheering for each of your creatures as you send them out to their death for your glory. Chaos Reborn recently passed through Kickstarter so there's a fancy new version in development and if you're willing to stuff a bunch of complicated stuff like inventories and questing and actual background images then there's always the phenomenal Lords Of Chaos that's well worth learning.
Wargames: Wargame: Red Dragon
The third in the Wargame series is the most comprehensive of the bunch, with air, land and sea units all represented in a kind of rock paper scissors battle system where you have to manage your supplies and ammunition along with formations and tactics. With limited units on the field and limited supplies of fuel and ammunition each helicopter sortie or missile fired has impact and meaning.
Racing: Sonic And Sega All Stars Racing Transformed
Starring a multitude of mascots and misfits from Sonic to Football Manager (yes,really) this cart racer is a modern, refined throwback to the glory days of Sega, with stages from Golden Axe and Nights Into Dreams, trans forming vehicles and power ups to be snagged from the track there's fun for the whole family and a varying degree of challenge that helps make the experience far less frustrating than Mario Kart often is. Whether you're a fan of cart racers or not, Sonic And Sega All Stars Racing Transformed deserves a look as it might just change your mind when you're pulling backflips as Alex Kidd in his gyrocopter.
Sports: Super Dodge Ball
Featuring everyone's favourite Kunio-kun this arcade game is a gloriously Japanese take on the oft maligned sport of dodgeball. While many versions and ports of Super Dodge Ball haven't made it outside Japan, the NES version adds a bit extra and if you can swallow the graphic and speed downgrade it's definitely the version to pick up for someone looking to bean a blocky bloke in the bonce with a ball.
Distributed in full on demo disks by Amiga Power and Amiga Format twice in 1993 and again in 1996 this turn based game sees up to four players placing single atoms in a grid, stacking multiple atoms to make them explode into adjoining squares for huge chain reactions with the aim of overwhelming your opponent. There's a rather excellent Linux version called KAtoms, but these days a Windows version is all but impossible to come by but since it was on a demo disk for free, it's not really piracy if you emulate it. Arr!
Massively Multiplayer Online Games: War Thunder
While not a personal favourite anymore, War Thunder has both air and ground combat at varying degrees of simulation and is sure to provide at least a few hours of enjoyment in each mode. It's also free so you've got nothing to lose by giving it a look.
Casual Games: Peggle
A gamified version of pachinko, Peggle offers up a fair few levels of colourful peg-tagging fun where you launch a ball down the board and hope you're not a bit crap at judging where it'll go. So very relaxing.
Music Game: Symphony
Symphony takes your music tracks and builds a shoot em up stage out of it. Upon completing the stage you get a weapon randomly generated from the games selection so you're always encouraged to keep playing looking for the elusive Furia weapons.
Party Game: Fortune Street
A more serious party game than Mario Party and more akin to Monopoly but maybe a bit less likely to ruin your friendships. Known as Boom Street in some territories and relatively easy to find, it's well worth checking out for board and party game lovers.
Programming Game: Hack & Slash
Your sword is a USB dongle, and slapping enemies and objects actually allows you to edit the variables in the games code. At first you feel like a god when you unlock a door or make an enemy weak and then you feel like a prat for accidentally summoning ten thousand turtles a second and crashing the game. For Zelda fans looking for something new or gamers after a quality adventure that'll make you think and feel good this is a must have.
Puzzle Games: Tetris
It's the progenitor of all puzzle games, the simple game of making lines out of shapes for points. Whether you play on the Gameboy or one of the many many derivative versions it's just not possible to topple Tetris from its celestial throne of best puzzle game ever. Alternatively, there's the Professor Layton games which aren't really puzzle games so much as games made of puzzles, they're also rather splendid.
Board Games: Talisman
A faithful computer recreation of the questing and conquering board game of the same name. The developers have poured a whole host of care into every aspect of the game to accurately digitize the hundreds of cards from characters to creatures to loot. Various rule sets are also supported, as well as house rules and expansion decks that introduce loads of new features. Offline and online play are supported too, so there's no safer way not to get punched when you land on your mate's tile and choose to take his gold in a fight.
Card Games: Chainsaw Warriors
Solitaire for geeks. You are Chainsaw Warrior, the Darkness is threatening the world and you're going to delve through two decks of perilous event cards with your chosen gear and trusty dice to mince zombies, rats and cultists all the while hoping you've got what it takes to pull the Darkness card and shoot him in the face with a sweet ass giant gun and save the day.