Since I have abso-fucking-lutely nothing to do with my time:
1991: Super Mario World (Super Castlevania IV)
1992: Sonic the Hedgehog 2 (Kirby's Dream Land)
1993: Sonic CD (Kirby's Adventure)
1994: Super Metroid (Sonic & Knuckles)
1995: Chrono Trigger (Warcraft II: Tides of Darkness)
1996: Metal Slug (Super Mario 64/Crash Bandicoot)
1997: Crash Bandicoot 2: Cortex Strikes Back (Lylat Wars)
1998: Metal Slug 2 (Crash Bandicoot 3: Warped)
1999: Metal Slug X (Crash Team Racing)
2000: Metal Slug 3 (Zeus: Master of Olympus)
2001: Grand Theft Auto III (Jak & Daxter: The Precursor Legacy)
2002: Warcraft III: Reign of Chaos (Metroid Prime)
2003: Warcraft III: The Frozen Throne (Grand Theft Auto: Vice City)
2004: Metroid Prime 2: Echoes (Ratchet & Clank: Up Your Arsenal)
2005: Resident Evil 4 (Sly 3: Honor Among Thieves)
2006: The Legend of Zelda: Twilight Princess (Guild Wars Nightfall)
2007: World of Warcraft: Burning Crusade (Metroid Prime 3: Corruption)
2008: Super Smash Bros. Brawl (Mario Kart Wii)
2009: Mario & Luigi: Bowser's Inside Story (N/A)
2010: Donkey Kong Country Returns (Mega Man 10)
2011: Minecraft (Kirby's Return to Dreamland)
Runner-ups are in brackets, if you didn't figure that out.
Also, I (obviously, since I was born in '96) didn't play each one of these in their respective release years. In fact, I played most of these for the very first time less than three years ago.
