I did five for each system to be fair. I think these include most of the game of the year nominees as well.
Gamecube
-Resident Evil 4
-The Legend of Zelda
-Donkey Kong: Jungle Beat
-Donkey Konga 2
-Pokemon XD
Xbox
-Jade Empire
-Conker: Live and Reloaded
-Forza Motorsports
-Oddworld: Stranger's Wrath
-Splinter Cell: Chaos Theory
PS2
-God of War
-Wanda and the Collossus
-Gran Turismo 4
-Final Fantasy XII
-Kingdom Hearts
PC
-Battlefield 2
-FEAR
-STALKER
-Age of Empires 3
You can fill these in because I know very little about PC gaming.
PSP
-Lumines
-Ridge Racers
-Wipeout Pure
-Grand Theft Auto
-Mercury
DS
-Animal Crossing DS
-Meteos
-Advance Wars DS
-Mario Kart DS
-Another Code
GBA
-Zelda: The Minish Cap
-Fire Emblem: The Sacred Stones
-Racing Gears Advance
-Klonoa 2
-?
Multiplatform
-Splinter Cell: Chaos Theory
-Brothers in Arms
-Grand Theft Auto: San ANdreas
-Psychonauts
-Doom 3
Gamecube
-Resident Evil 4
-The Legend of Zelda
-Donkey Kong: Jungle Beat
-Donkey Konga 2
-Pokemon XD
Xbox
-Jade Empire
-Conker: Live and Reloaded
-Forza Motorsports
-Oddworld: Stranger's Wrath
-Splinter Cell: Chaos Theory
PS2
-God of War
-Wanda and the Collossus
-Gran Turismo 4
-Final Fantasy XII
-Kingdom Hearts
PC
-Battlefield 2
-FEAR
-STALKER
-Age of Empires 3
You can fill these in because I know very little about PC gaming.
PSP
-Lumines
-Ridge Racers
-Wipeout Pure
-Grand Theft Auto
-Mercury
DS
-Animal Crossing DS
-Meteos
-Advance Wars DS
-Mario Kart DS
-Another Code
GBA
-Zelda: The Minish Cap
-Fire Emblem: The Sacred Stones
-Racing Gears Advance
-Klonoa 2
-?
Multiplatform
-Splinter Cell: Chaos Theory
-Brothers in Arms
-Grand Theft Auto: San ANdreas
-Psychonauts
-Doom 3