Action: God of War
FPS: Half Life 2
TPS: Resident Evil 4
Racing: Gran Turismo 4
JRPG: Chrono Trigger
WRPG: ES4: Oblivion
Adventure: Shadow of the Colossus
Action Adventure: Metroid Prime
Platformer: Super Mario Galaxy
Fighting: Tekken 3
Music: Guitar hero 3
Party: Warioware Smooth Moves

Action-Adventure- God Of War I, II 

Role Playing Game- Final Fantasy VIII

Puzzle- Hexic

3D Fighter - Tekken 3

2D Platformer -Oddworld: Abe's Oddysee

3D Platformer-Super Mario Galaxy

First Person Shooter- Halo

Third Person Shooter- Resident Evil 4

Survival-Horror- Resident Evil 3

Racing- Mario Kart DS, Speed Freaks

Simulator- The Sims + Expansions

Music- Guitar Hero III

Party- Guitar Hero III

FPS: halo, Golden Eye
TPS: GeOW
WRPG- Fable, Jade Empire
JRPG-baten kaitos, Skies of Arcadia
Fighters- Marvel vs. Capcom, Power stone
Action- Crackdown, Ninja gaiden, Jet set radio future,
Action-adventure- LOZ: OoT, GTA 3
Platformer- Sonic Adventure, Ratchet and Clank: up your arsenal
Music- Samba de Amigo, Rock band
Survival Horror- Condemned, Resident Evil 4

Action-Adventure: zelda tp
Rpg: gladius
Puzzle:Tetris
Fighting:ssbb
Platforming:Super Mario Galaxy
Fps: red steel
Tps:???
Light Gun-ReUC
Shoot em up???
Survival-Horror: resident evil remake
Racing:mario kart dd
Simulator:cooking mama
MMO:???
Music???
Party: mario party 8
Sports-Wii sports

Action-Adventure: LoZ OoT

JRPG: Final Fantasy 5 (Yes, 5.)

Puzzle: Tetris

Fighting: Marvel vs Capcom 2

Platforming: Sonic 2

FPS: Half-Life

TPS: RE4

Light Gun: House of the Dead (Typing of the Dead is even better, but no gun. ^^;)

Shoot em up: Metal Slug (hard to pick one)

Survival-Horror: RE4?

Racing: GT4 (or maybe GT2)

Simulator: GT4? (It is the "real racing simulator" XD)

MMO: Albatross18/Pangya (Not sure if it qualifies, but it's as close as I'm willing to get)

RTS: Age of Empires 2

Music: DDR (Again, hard to pick one.)

Party: Wii Sports? (Does this count? I don't really play party games.)

Sports: NBA Jam(Genesis version. Wii Sports seems like a different genre somehow.)

Action-Adventure:LoZ OOT
Rpg: Chrono Trigger
Puzzle:Tetris
Fighting:Don't really play but SC2
Platforming:?
Fps:COD4
Tps:Mass Effect
Light Gun-
Shoot em up-
Survival-Horror: Jericho
Racing:NFS Underground 2
Simulator:The Sims 2
MMO:
Music:GH3!
Party:
Sports-NBA Streets Homecourts

Adventure: LoZ: OoT

RPG: KOTOR

Puzzle: Picross DS

Fighting: Street Fighter 2

Platforming: Mario 64 (Is it really a platformer?)

FPS: Halo Combat Evolved/Goldeneye 007

Light Gun: Virtua Cop 2

Racing: Daytona USA

RTS: Age of Empires 2

Sports: Wii Sports

Action/Adventure: Ninja Gaiden Sigma.

RPG: MS Saga: A new Dawn.

Platformer: Super Mario World.

Fighting: Capcom vs SNK 2.

First Person Shooter: Call of Duty 4

Puzzle: Bean Machine.

Third person shooter: Resident Evil 4

Racing: F-Zero 64

Sports: NBA Ballers.

Action/Adventure: Ocarina of Time
Fighting: Super Smash Bros. Melee
TPS: RE4
FPS: Timesplitters Future Perfect
Lightgun shooter: Umbrella Chronicles
Horror/Survival: REmake
3D Platform: Super Mario 64
2D Platform: Jazz Jackrabbit 2 ;)
RPG: Tales of Symphonia
Racing: F-Zero GX
Sports: SSX Blur
Puzzle: Zack & Wiki
Punk: No More Heroes (just had to mention it)

Action/Adventure: Double Dragon
RPG: Oblivion
Platformer: Super Mario Bros 3
Fighting: Street Fighter 2
Puzzle: D/Generation
First Person Shooter: Unreal Tournament 3
Third person shooter: (*)
"What used to be called a Shooter": R-Type
Racing: Wipeout 3
Sports: Smash TV (probably doesn't count)

(*): I'm still holding out and will until the end of time for Commander Keen 3D.