2000 - Legend of the Dragoon
One of my gateway games to the world of RPGs. I'll admit it doesn't hold up as well nowadays, but I can still replay it without a problem and have fun with it.
2001 - Tie: Smash Bros. Melee / MGS2
It's too hard a split this year because both games threw me for a loop in very different way. Melee skirted the line between competitive fighter and party game, and I'll admit that I had my core group of friends who constantly tried to one up the other. MGS2 was... well, MGS2.
2002 - Tie: Kingdom Hearts / Metroid Prime
An action RPG with disney characters? A first person Metroid game? Both of these were hard sells, but the exection was simply magical. Hell, Kingdom Hearts was my reason to own a PS2... the Final Fantasy cameos helped!
2003 - Fire Emblem
"lol, is this the game with Roy??" is a phrase I'll never stop shuddering it cause of this game. Fire Emblem's GBA venture is arguably still the best.
2004 - Katamari Damacy
This game taught me that a simple, refined concept polished to perfection can end up a better game than a complex game that plays like shit. It helps that the world of Katamari is fucking nuts... the good kind, anyway.
2005 - Devil May Cry 3: Dante's Awakening
Kinda cheating here since the Special Edition is the one I really love, but this game put Dante on the map for me and still is my favorite action game of all time, no contest. I'll never be as good at it as the likes of other players, but that doesn't stop me from striving to up my game when I can.
2006 - Tie: Kingdom Hearts II / Ace Combat Zero: The Belkan War
While not the ideal the direction for the series, KHII is an absolute joy to play, improving on the first game in nearly every aspect. Ace Combat Zero is the best game in the series in my opinion, with the tightest controls, perfect balance in difficulty, short enough but highly replayable, and music that gives Ace Combat 4 a run for it's money.
2007 - Persona 3
Not an entirely popular opinion, but this is my favorite between P3 and P4, for minor reasons for another thread on the matter. I do credit it for introducing me to SMT in general, so there's that.
2008 - Persona 4
...Not to say that I also don't really like P4.
2009 - Tie: BlazBlue: Calamity Trigger / Demon's Souls
The former is probably an uncommon opinion, but BlazBlue was what got me into fighting games period. I didn't bite on Street Fighters of years past, I didn't think of 3D fighters like Tekken as more than an occasional game with friends, and I simply didn't find much interest in the practice. That all changed with this game, and I've been a fan and supported of the genre ever since.
Demon's Souls is... well, Demon's Souls.
2010 - Kingdom Hearts Birth by Sleep
Three KH games on the list may seem like overkill, but I really like this series ok.
2011 - Ultimate Marvel vs. Capcom 3
The greatest crossover of all time returns. It's mahvel baby.
2012? - Tie: Gravity Rush / Persona 4 Arena / Katawa Shoujo
Too many feels with too many games.