If excluding game collections;
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NES - Super Mario Bros. 3 (How original...)
Game Boy - Tetris
Sega Mega Drive - Sonic & Knuckles
SNES - Super Metroid (Also, to this day, my favorite video game in existence.)
Sony Playstation - Final Fantasy IX
Nintendo 64 - The Legend of Zelda: Ocarina of Time (Another really original choice.)
Sega Dreamcast - SoulCalibur
Game Boy Advance - Mario & Luigi: Superstar Saga
PC - Warcraft III: Reign of Chaos
Playstation 2 - Shadow of the Colossus
Gamecube - Metroid Prime
Xbox 360 - Bioshock
Playstation 3 - LittleBigPlanet
Wii - Super Mario Galaxy 2
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If collections are included however, my favorite PC game would have to be The Orange Box, and the honor of my favorite Wii game would go to Metroid Prime Trilogy.