Stategy: Age of Empires 2. That's the only game this list needs.
RPG: Arcania: Gothic
MMO: Last Chaos
Shooter: Duke Nukem Forever
Strategy: Tom Clancy's EndWar
action: Postal 3
stealth: Assassin's Creed 3
Racing: Big Rigs: Over The Road Racing
Sports: Ashes Cricket 2013
RPG: Mass Effect 2
Shooter: Return to castle Wolfenstein
Strategy: Red Alert 1
Action: Dead Space 1
Racing: Monster Truck Madness 2
Strength Determination Merciless Forever
RPG: DAO/witcher 2
Shooter: bf genre.
Action: Batman games
Stealth: dunno havent played any
Sports: havent played any.
My favorite genres are RPG and strategy (turn based or building and god games)
RPG: Skyrim or Dragon age 2, hard to pick
MMO: WoW and Runescape. I dont play the latter any more though but I used to when I was little and loved it.
Shooter: Hard to say, I dont usually play shooters, Dead Space 3 maybe, cant think of any others.
Strategy: Might and Magic Heroes 6 (again so many games so it's hard to pick)
Action: Assassins creed Black flag (this so much:P even though it feels and plays more like a RPG)
Stealth: This is a separate genre now? Oh well, Dishonored
Racing: Never played one and probably never will
Sports: Same as above
Shooter: Maybe BF
Action: AC series
Sports: NBA2K and Madden NFL
Excuse me, are you saying something? Nah, you can't tell me nothing
RPG: Might & Magic VII (that Time when it came out I hadn't played anything that captivating and epic, and I haven't seen any other game top that feeling)
Shooter: Quake 3
Strategy: Jagged Alliance 2
action/adventure: Fahrenheit: Indigo prophecy
stealth: Metal gear solid
Racing: Colin Mcrae Rally 2
Sports: Fifa street
Looking at the OP's games I'd say he's a very young gamer. Or hasn't played many games.
RPG: Mass Effect + KotoR + Dragon Age series (can't pick the best of them as I love them all).
MMO: Ultima Online
Shooter: Star Wars: Jedi Knight series
Strategy: Age of Empires 2 (single player), Starcraft 2 (multiplayer)
Action/Adventure: Gobliiins 2
Stealth: Deus Ex: Human Revolution
Racing: Wacky Wheels (no kidding!)
Sports: Chessmaster 5000
Card games: Etherlords 2
Platformer: Tyrian 2000
RPG - Castle of the Winds
MMO - WoW
Shooter - Half-life
Strategy - Starcraft (C&C Red Alert very close 2nd)
action/adventure - N/A
Stealth - N/A
Racing - N/A
Sports - N/A
MMO: vanilla WoW
Shooter: CoD1 (Best shooter to date, best community, best shoutcasts, best fragmovies http://www.youtube.com/watch?v=W1QISjR4qtE)
RTS: C&C Yuri's revenge
Action: Mass Effect 1/2/3
Stealth: Splinter Cell 1/2/3 (Recent versions are a joke, mark targets and gg press 1 button, not to talk about the terrible new voice of Sam) Too bad Pandorra tomorrow is ommited on every box-sets because the game apparently doesn't run on windowsxp and upwards.
Racing: Need for Speed Underground 2 (with the giant worldmap)
Sports: FIFA 99, before fifa became scripted to the max and the "fair play" bullshit got introduced, so no more red-card button, or the dive-button (which was amazing).
RPG: Final Fantasy VII
MMO: World of Warcraft
Shooter: Halo: Combat Evolved
Strategy: Fire Emblem: The Sacred Stones/Warcraft III (Turn based and RTS separated)
Action: Legend of Zelda: Ocarina of Time
Stealth: Assassin's Creed (More of the series as a whole)
RPG: Chrono Trigger - 1995
MMO: World of Warcraft - 2005 and still in development
Shooter: Halo 2 - 2004
Strategy: Advance Wars 2 - 2003
Action: Diablo 3 - 2012
Stealth: Splinter Cell - 2002
Racing: GranTurismo 2 and 3 - 1999 and 2001
Sports: NBA Street
Jump and Run: Rachet and Clank 3 - 2004
Most Played Game: Propably World of Warcraft, Dota (Wc3) and Heroes of Newerth
Most Played System: Computer
MMO: EverQuest (classic)
Strategy: Total War Rome 1
RTS: StarCraft: Brood War
RPG: Diablo/Legacy of Kain franchises
Shooter: Wolfenstein/Quake/Doom/Half-Life franchises
Strategy: WarCraft 3/StarCraft 2
Action: God of War franchise
Based on what I've played... Maybe not "best" but they are my favorite... And yes I ignored the "PC only" because I haven't played most of those genres on PC...
RPG: Final Fantasy 7
MMO: WoW I guess...
Strategy: Warcraft 3 TFT
Action: Diablo 2
Stealth: Metal Gear Solid 2
Racing: Mario Kart 64
Sports: Tiger Woods
RPG - Fallout 3, hell, that's my vote on the best game ever made. And best DLC ever made, short, but they felt like different video games, and that was an amazing feeling.
MMO - The Secret World. It's one that sticks out for me, it's very unique in the MMO genre, and not just another Warriors and Wizards vs Dragons.
Shooter - Best 3rd person, Mass Effect (first one) Best first, Halo on the PC. Best memories.
Strategy- Civ franchise.
Action - Bayonetta
Racing - Trackmania. So addicting. Love Canyon the most because of the drift.
Sports. Eh...NBA Street on the gamecube, 100% that thing, fun as hell.
Stealth - This one will be an odd ball, but I will go on ahead and say Skyrim, maybe even the whole Elder Scroll series because that's all I play in that game, a rogue that takes their time to kill their targets one by one.
RPG: Chrono Trigger
Shooter: Half-Life 2
Action: Resident Evil 4
Stealth: can't think of anything
Racing: Mario Kart
Sports: Blades of Steel
RPG: The Elder Scrolls V: Skyrim
MMO: World of Warcraft
Shooter: Call of Duty: World at War
Strategy: Tropico 4
Action: Portal 2
The new box art for Blizzard's upcoming game; Overwatch!