And give a short explanation why. (NOTE: this is an opinion list, not an objective list. You aren't trying to say what the best game is in each category. Just your personal favorite.)

FPS (Single Player):
FPS (Multiplayer):
RPG:
TBS:
MMORPG:
Action/Hack-n-Slash:
Fighting:
Racing:
Platformer:
RTS:
Adventure/Point-and-Click:
Casual:
Other (Anything that doesn't comfortably fit in any above category):


for me:

FPS (Single Player): Painkiller. This is a hard choice, since FPSs are really MY genre. But I'm going to have to go with Painkiller. With amazing level designs, creative enemies, awesome weapons, evocative music, a surprising amount of depth, and always fun gunplay, I think I have to rank it as my favorite FPS.

FPS (Multiplayer): AvP1. It's unbalanced, kinda dead, and weird. But it's SO MUCH STINKIN FUN. Actually being able to stalk people as the Alien and Predator...the feeling of horror as the marine... the ridiculously fast pace... it's all just awesome.

RPG: Morrowind, currently. I don't have a lot of experience with RPGs, and I'm not very good at them, but Morrowind's entertainingly open-ended world and plethora of places to explore have won me over. This might change after playing more than 10 hours :3.

TBS: X-COM X-COM X-COM! An amazingly deep game with some of the most intense TB battles out there.

MMORPG: Erm...haven't really played any.

Action/Hack-n-Slash: Diablo II. A deep looting system and attention to little gameplay details makes grinding tons of fun, and taking out hordes of baddies is quite satisfying.

Fighting: Super Smash Brothers Melee. I don't like fighting games...competitive fighting games, that is. SSBM is just chaotic insanity. Which is why I love it.

Racing: Have really only played Mario Kart, and I'm loathe to put that as my favorite :P.

Platformer: New Super Mario Brothers Wii. It's just... I don't know. So fun. Loads of secrets, beautiful visuals, that irresistible music...

Adventure/Point-and-Click: Machinarium. This game is simply perfection. It encompases everything that is great about P&C games and has a phenomonal artstyle and sound effects to boot. Myst is a close runner-up.

Open World: Red Faction Guerrilla. It may not have the same zany quality as GTA or Saints Row, but I found that RFG's fully destructible world and satisfying gunplay proved to be a winning combination for me.

Casual: Tetris. Do I even need to explain why? The grandaddy of all casual games still ranks as one of the most addictive experiences out there.

Other (Anything that doesn't comfortably fit in any above category): STALKER Call of Pripyat. Part visceral shooter, part open world, part RPG, part horror, and all awesome. STALKER is one of the best series of the entire generation. And I find CoP to be the best STALKER game. You can do the math :3

EDIT: oops, forgot RTS! Added to the list. For the record, my fav is probably Age of Empires II.

EDIT 2: urg. Forgot TBS too.

EDIT 3: gah! How could I forget platformers???

FPS (Single Player): Quake 4
FPS (Multiplayer): Halo 3
RPG: Morrowind (I havn't played the new elder scrolls)
MMORPG: StarWars: The Old Republic
Action/Hack-n-Slash: Diablo II
Fighting: DOA 4
Racing: NFS Carbon
Adventure/Point-and-Click: Havn't really played one..
Casual: Tetris
Other (Anything that doesn't comfortably fit in any above category):
RTS: Starcraft 2

FPS (Single Player): Far Cry

FPS (MultiPlayer): Halo Reach (I've never done much multiplayer except with friends)

RPG: Gothic 3 or The Witcher (after community patch of course)
MMORPG: reality, I don't have time for it, so I pretend to be a ninja and sneak through my house, unfortunately my wife has a built in detect life spell, and I can never get past her

Action/Hack n Slash: Prince of Persia series, or Ocarina of Time

Fighting: Street Fighter 2

Racing: Burnout Revenge

Adventure/Point-and-Click: haven't played any

Open World: Either STALKER: Shadow of Chernobyl or Skyrim

Casual: Bejeweled

Other: Civilization III

FPS (Single Player): Half-Life 2
FPS (Multiplayer): Counter-Strike: Source
RPG: Baldur's Gate 2
TBS: Civilization IV
MMORPG: N/A
Action/Hack-n-Slash: Titan Quest
Fighting: Super Smash Bros Brawl
Racing: DiRT 3
Adventure/Point-and-Click: The Curse of Monkey Island
Open World: The Elder Scrolls V: Skyrim
RTS: Starcraft
Platformer: Super Mario 3
Casual: Minesweeper
Other (Anything that doesn't comfortably fit in any above category): System Shock 2 (FPS/RPG/Survivor horror hybrid), X-Com (Turn-based tactics), SimCity 4 (City simulation)

FPS (Single Player): Half-Life 2 (+ episodes)

FPS (Multiplayer): idunno.. Counter Strike or Black Ops maybe.. i'm not a big multiplayer gamer

RPG: It's a close one between Oblivion and Skyrim

MMORPG: Age of Conan i guess.. only one i played beyond level 30

Action/Hack-n-Slash: God of War (series)

Fighting: Tekken (series)

Racing: ermm.. Mario Kart.. if that counts.. i'm not into racers

Adventure/Point-and-Click: Sam and Max (series)

Casual: Angry Birds

Other (Anything that doesn't comfortably fit in any above category):
Uncharted 2 (TPS)
Metal Gear Solid 4 (stealth)

Off the top of my head..

FPS (Single Player): Blood
I played it earlier this year, and it was the only FPS in a very long time that has really made me super happy and excited. I was so excited that I forgot if I ever liked some other FPS more.

FPS (Multiplayer): Half Life 1 with mods
Stuff like Science & Industry and Sven Co-op were the best thing ever. Been a while since, but it was good

RPG: Planescape Torment
Goosebumpsies. The story, man, the story.

MMORPG: there was some Korean one that some guy made me try once, and that's the only one I've ever played so probably that. whatever it was. because it's the only one I've played. it wasn't very fun.

Action: Oni
Great gameplay, great music, great visual style, combat and weapons are fun, I like the characters, I like the story, and I want it on GOG just so I can tell people to buy it.

Fighting: Soul Calibur 2
My Raphael-play gave my friends a headache.

Racing: Chocobo Racing
It's so easy to cheat in this game, but it's fantastic and cute and happylappy. You get to customize your own driver too (color swap & attributes), after you beat the story mode.

Adventure: Grim Fandango
If you don't know why and haven't played it, I urge you to play it.

Casual: Sudoku
It gives me a sense of accomplishment after just staring at a bunch of numbers for a long time. Actually, does that even count as casual? Sometimes it hurts my brain a lot.

/edit: added some clarity to the Grim Fandango one.

FPS (Single Player): Bioshock
FPS (Multiplayer): Call of Duty 4 (Guilty pleasure, but I haven't played it in a long while)
RPG: Oh... uh... Persona 4? Risen? Thats way too difficult to answer
MMORPG: LOTRO
Action/Hack-n-Slash: Titan Quest
Fighting: BlazBlue for it's amazingness OR Soul Calibur 2 for it's story mode.
Racing: Blur was great at the last LAN party I had. Otherwise, Need For Speed 2.
Adventure/Point-and-Click: Machinarium, easily. However I really love the Gemini Rue/Beneath a Steel Sky stlye.
Casual: PEGGLE. YES.
Other (Anything that doesn't comfortably fit in any above category): Robin Hood: The Legend of Sherwood

HEY WHERE THE HECK IS MY STRATEGY AND RTS?!

RTS: Command and Conquer. It beats Age of Empires by a bit.
Strategy: Medieval 2: Total War LOTR total conversion (I know there is an RTS element, but thats not the part I love about it) OR Civilization 5.

FPS (Single Player): Unreal Tournament Gold Edition - whilst the latter games in the series have added vehicles this was the golden game that started it all (for me at least) and many favoured maps and overall gameplay are hard to beat

FPS (Multiplayer): - blank

RPG: Baldur's Gate 2 - for the shear depth of story and interactions on offer; characters in a party that are not just dead sprites that obey your every command; differences of opinion mixed with a very non-linear world (story is linear, which help when telling many good stories, but the world itself is quite open). It's also not afraid to kill you and make you reload and retry

MMORPG: - eh never really gotten to grips with these, but Guild Wars for the fact that its not all about playing till you're a zombie to get to left 90.

Action/Hack-n-Slash: - Diablo 2 - few have managed to mix the same amount of fun, slashing, hacking and random map generation of this title. Some have come close, but many have maps far to linear for their own good (yes I'm looking at you Torchlight) whilst others have stories just not involving nor gripping enough (looking at you Sacred and your daft sidequests)

Fighting: - blank

Racing: - blank

Adventure/Point-and-Click: - blank

Casual: - Minecraft *need I say more?*

ALSO this list totally missed out RTS and Turn based Strategy as well as the 4*Genre - 3 big areas you can't leave out!

RTS - Very very hard to pick just one that fits as the top of all time and I'm tempted to just put my first Starcraft; though honourable mentions must go to Homeworld, Warcraft 2, Total Annihilation, Empire Earth and others

Turn based Strategy - Disciples 2 Rise of the Elves - though I'' admit I've not many on my table here, but Rise of the elves represents the most fun I've had with one and certainly a good all round title; even if it has a few weakpoints (like being closer to a turn based party game with regard to experience). Disciples 3 might push in here if the revelations about the upcoming standalone release prove to be as good as they are rumoured to be.

4* Genre - your big epic and typically turn based empire building and what better game than to put Imperium Galactica 2 in here. One of the few to really match both empire building; fleet and ground strategy battles and also a bit of colony building as well. A game all to its own with what it offers and about the only one that really offers ground combat as opposed to numbercrunching which most feature.


Also Total War series belongs in there somewhere both for its turn based map battles and for its real time troop fights; one of the few if only games that really lets you fight well with large numbers of units on the battlefield (Even the much talked about Supreme Commander could learn a thing or two about big fights from Total War)

oops, you've forgot about other type strategy games! Two types of FPS and no TBS?! what about adaptations of board games? :/ Discrimination....

BTW: I'm not going to fill this as I'm mostly playing TBS, so I do not have some strong favorites in other genres :P

I have to second this. A lot.

From a pure game design/theory perspective, Tetris could be the perfect game. It's rules are few and simple, but it gets incredibly deep and is infinitely replayable. Plus it rises beyond gaming genres and tastes, and is probably the one game that is valued by humanity as a whole and not just by forum-dwelling gamer nerds.

I'll try, but it's going to be tough.

FPS (Single Player): Outlaws, because i'm not a great fan of FPS in general but a sucker for Spaghetti Western and I like the cartoony style, the atmosphere and the music.

Action/Hack-n-Slash: Maybe Nox, at least from my memories (I don't know if I'd still like it as much today), because at that time I liked that the combat included well-timed keyboard actions instead of just mouse clicking and although the combat was a lot of fun, IIRC the game wasn't that heavy on grinding and offered other motivations, too (to this day I haven't completed neither Diablo II nor Torchlight, due to a lack of motivation, but I had no such issues with Nox).

RPG: Planescape Torment, because for me acting a role and being part of an awesome story with character progression also in a literal sense has always been more attractive than learning complicated rules and juggling with numbers. And the setting and atmosphere are some of the best. And no clichéd standard fare fantasy (or at least less than in other RPGs).

Fighting: Depending on the definition, but since I don't play many beat-em-ups, I'd say Castle Crashers. It's both fun and funny, has a great style and soundtrack and enough replay value.

Racing: Wacky Wheels. C'mon, you can throw hedgehogs at each other. :D

Adventure/Point-and-Click: Can't really answer this one, too much choice. Of the classics, maybe Monkey Island 2 or Day of the Tentacle, but then there's also Sam & Max Hit the Road, Grim Fandango ... Of the more recent ones I most enjoyed Time Gentlemen Please.

Casual: Currently Blocks that Matter, I think. The levels are clever puzzle diversions for a few minutes.

FPS (Multiplayer), MMORPG, RTS, Strategy: Hardly any experience with these kinds of games, I admit.

You forgot Platformer: Psychonauts. Most original and varied platformer I've played, despite some frustrations.

Other: Hm... maybe Enclave. Although you could describe it as fantasy FPS. Or Beyond Good and Evil. Although it's actually in the same category as Psychonauts and I only try to smuggle it in here so I can nominate two platformers. :P

Frankly, there are too much great games for me to create a truthful "favorite" list, I'm a pretty promiscuous gamer. ;)

FPS (Single Player): DOOM, hands down. You all know why DOOM is the best. I have yet to beat the first one, currently at around. E3M5 or so, so if DOOM II is better, which I know some say so, I can only put the first one here.

FPS (Multiplayer): Hmm... Tough one. Quake III? Brink? No idea.
Halo CE comes in before that, for both FPS categories (I have no Xbox, so I play the PC version, which has online multiplayer)

RPG: Not a big RPG fan, but Fallout 3 has to be the best RPG ever, IMHO.

MMORPG: Haven't played many. I played WoW for at least 20 minutes, then never touched it again, except to uninstall it!

Action/Hack-n-Slash: Never really played any hack-and-slash games. Am I a sad creature for not playing even a little Diablo II?

Fighting: Street Fighter II. Aw HELL yeah! My friend is more of a Mortal Kombat guy, but I totally prefer Street Fighter more, because I just can't pull off fatalities, even though it isn't usually much harder than doing Hadokens and Shoryukens. I just beat the whole championship/campaign/etc. in one sitting yesterday, and I had a blast! Can't wait to try to get a hard copy of it for my Genesis (I have no SNES) and another 6-button controller for it, maybe that sexy beast of an arcade stick, so I can play 2-player with people! Even holding my own 6-button controller makes my hands feel the craving to use the controller on some Street Fighter II!

Racing: I. Hate. Racing. But what I do kinda like is that one Mario Kart for the GBA. :P

Strategy: I have a soft spot for RTSes, but I have yet to get and play any I'd prefer to mention. Maybe Revenge of the Titans, even though it's just a tower-defense, it's the only strategy game I'd prefer to mention.

Adventure/Point-and-Click: The only point-and-clicks I've played are some of the Telltale ones (Sam and Max, Abe Lincoln Must Die being all I've played, but I desperately want more) and Broken Sword 1 that became a freebie for a while some time ago, I've been meaning to play BS:SotT for some time now, since I just beat Mega Man 2 last week, but I'm not in the mood.

Platforming: I'll just settle for Sonic 2 with a tie for Mega Man 2. Sequels rock!

FPS (Single Player): Stalker : Shadow of Chernobyl with the Stalker Complete 2012 Mod

FPS (Multiplayer): N/A. Never did play multiplayer except with bots.

RPG: Dungeon Crawl Stone Soup (Tiles Version) if roguelikes are counted as RPGs. Elegant UXP out of the box (and it's free!) Otherwise Exit Fate for the story and sheer number of collectable allies.

MMORPG: Legacy of Thousand Suns. A Facebook MMORPG-lite if those "games" count. The item descriptions are a hoot.

Action/Hack-n-Slash: N/A!

Fighting: N/A! Haven't played any fighting games on a PC for a long while.

Racing: NFS Underground 2 when I want to race at high speeds. Bonus points for the option to make your ride impossibly ugly. Colin McRae Rally 2 for the simple joy of virtual driving.

Adventure/Point-and-Click: N/A. Tried but just too impatient to enjoy this genre.

Other:

Flight Sim: Enemy Engaged - Comanche vs Hokum - Fly low and pop up to blow enemy armor to bits. Escort assault helos capturing an airbase. A living battlefield on which your actions during a mission actually counts.

Turn-Based Tactics: Panzer General 3D Scorched Earth - Combined arms combat that's much more fluid than PG1 / Panzer Corps. The difference that allowing a unit to move multiple times in the same turn makes … The UI is significantly simplified as compared to its predecessors.

Real-Time Strategy: Total Annihilation - The number of options to crush your enemy is mind-boggling. It's also much more manageable than Supreme Commander due to the reduced scale. The excellent music score makes it one of the few games that I don't turn off the music.

Real-Time Tactics: Legion Arena - Think of it as Rome Total War without the strategic layer and tack on linked scenarios and RPG mechanics for unit upgrades.

Shmup: Jets N' Guns - Blow things up! Buy upgrades! Blow more things up!

FPS (Single Player): Painkiller was pretty badass.

FPS (Multiplayer): I'm a single-player kind of guy, but Team Fortress 2 I guess.

RPG: Classical RPG? Have to go with Fallout 2

MMORPG: Don't play any.

Action: Metal Gear Solid.

Hack-n-Slash: Diablo 2. Easy.

Fighting: Eh.... Street Fighter 2.

Racing: Not much for racers, but I did spend an ungodly amount of hours on Gran Turismo 3.

RTS: Constructor. Not the best by far, but my favourite.

Adventure: Heavy Rain

Point-and-Click: Broken Sword.

Casual: Peggle!

Other (Anything that doesn't comfortably fit in any above category): I'll totally list a good amount of other genres!

JRPG: Final Fantasy X

Platformer: Super Mario World

Puzzle-platformer: Braid.

Action platformer: Tossup between Castlevania, Super Castlevania IV and Castlevania: Aria of Sorrow.

Turn-based Strategy: Sid Meier's Colonization (the old one)

Simulator: Football Manager 2011.

Puzzle: Hmm, hard one... I think I'll give it to Picross 3D, with honorable mentions to The Lost Vikings and Portal.

FPS (Single Player): - Goldeneye
FPS (Multiplayer): - Goldeneye
RPG: - Mass Effect 2
MMORPG: Haven't played one!
Action/Hack-n-Slash: Sacred/Dynasty Warriors 3/4/5
Fighting: Street Fighter II
Racing: PGR series
RTS: Don't have a favourite RTS game.
Adventure/Point-and-Click: Broken Sword: Templars
Casual: Pokemon Blue - Pearl
Open World: Just Cause 2
JRPG: Chrono Trigger
Platformer: Comix Zone/Sonic3
Simulator: Pro Evolution Soccer 2009
Puzzle: Columns