This was harder than I thought.  Still not sure on some.

NES: Crystalis

SNES: Yoshi's Island

N64: Zelda Majora's Mask

Gamecube: Super Smash Brothers Melee

Wii: Super Mario Galaxy 2

Gameboy: Pokemon Red

Gameboy Advance: Fire Emblem

DS: The World Ends with You

PC: Oblivion

Genesis: Streets of Rage 2

Jaguar: Cybermorph

*** Means I don't remember or know, all systems listed I own/owned.

Tough Question!

2600 - Space Invaders

NES - Ninja Gaiden

Ps1 - Suikoden 2

PS2 -  Growlanser Geneations

GC- WindWaker

Wii- Super Mario Galaxy

PC- Space Quest 4

GB- Donkey Kong Land

GBC- Zelda-Oracle of Ages

GBA- Tactics Ogre

DS- Phoenix Wright Ace Attorney

PSP-Star Ocean: Second Evolution

hmm lets see

Atari 2600 - Pit Fall

GB - Gremlins 2 "loved that game"

GBA - xXx (awesome sidescrolling action game based on a movie)

DS - Yu-Gi-Oh series

NES - SMB3

skipped a gen and went to the 64 era

N64 - Golden Eye 64 or Ocarina of Time (i had to pick 2)

GameCube - Ahhh honestly i dont have a clue, i didnt own that many games and mostly gamecube games that i owned aint that good and they are mostly sport games because thats what i was into back then lol

Wii - No More Heroes franchise, Resident Evil Darkside Chronicles

ps3 - Uncharted franchise and Heavy Rain

Nice choice. You managed to skip the best video game generation of all time. (For me, at least.)

Saturn- Nights into Dreams

Game Gear- Sonic Triple Trouble

Dreamcast- Sonic Adventure

WiiWare- Cave Story

N64 Mario Kart 64

Gamecube- Metroid Prime

PS2 Dragon Quest 8

GameBoy- Tetris

Gensis- Sonic the Hedgehog 2

GameBoy Advance- THe Legend of Zelda The Minish Cap

Playstation- Crash Bandicoot 2

Wii- New Super Mario Bros Wii

DS- New Super Mario Bros DS

SNES- Donkey Kong Country

Nes- Super Mario Bros. 3

I left out Atari 2600 and depending when im asked they might change around a little. Most diffently the Snes one.

Sony

PS1: Crash Bandicoot 3: Warped

PS2: Kingdom Hearts 2

PS3: Uncharted 2

PSP: Tekken: Dark Resurrection

Nintendo

SNES: Mario Kart

GameCube: Mario Smash Football

Wii: Super Smash Bros. Brawl

GameBoy: Super Mario Land

GBA: Pokemon Leaf Green

DS: The World Ends With You (my absolute favourite of all time!)

Atari 2600: Space Invaders
NES: Super Mario Bros. 3
Super NES: Super Mario World (Donkey Kong Country is very close)
N64: Goldeneye
Gameboy: Pokemon Red
Gamegear: Bubble Bobble
Dreamcast: Powerstone 2
Gamecube: Eternal Darkness
Xbox 360: Gears of War 2
DS: Mario Kart DS
Wii: NSMB Wii
PC: Starcraft

NES - Kirby's Adventure
SNES - Secret of Mana
N64 - Kirby 64
GC - Super Smash Bros. Melee
Wii - Super Smash Bros. Brawl
WiiWare - Icarian: Kindred Spirits (hey, thats how its called on my Wii )

GB - Pokemon Silver
GBA - Fire Emblem: The Sacred Stones
DS - Tales of Innocence (so far, only played 4 games and I just got a DS recently)

SMD - Phantasy Star IV
SCD - Lunar Eternal Blue
Saturn - Grandia
Dreamcast - Grandia II

PS1 - Parasite Eve (I'd put Grandia here but thanks to it being a port, I can do otherwise)
PS2 - Ico
PS3 - Uncharted 2

PSP - Lunar: Silver Star Harmony

PC - Diablo 2: Lord of Destruction

360 - Tales of Vesperia

NES: Super Mario Bros. 3

SNES: (A tough one but the award goes to...) Chrono Trigger

N64: Mario 64

PS: Final Fantasy VII

DC: Resident Evil: Code Veronica

GC: Resident Evil 4

PS2: Final Fantasy X

Wii: Super Smash Bros. Brawl

PS3: Uncharted 2: Among Theives

PC: Starcraft: Brood War