Okay, I'm going to make a list of purely what I believe, even though my tastes are fairly odd sometimes.
Game of the Decade
Patapon 2: Yes, I know this game is a lot less high-profile than most of the other things people are saying, but the innovative gameplay, the fact it really added on the first game, the great art style and the best original soundtrack I've seen in a long time, this takes the cake.
FPS of the Decade:
Half Life. Okay, I don't need to explain this one that much.
MMO of the Decade:
WoW. I mean, there's only one to honestly choose from. =P
RTS of the Decade:
I have never been a big fan of this genre, so I'm passing here to.
RPG of the Decade:
Final Fantasy 5 Advanced. Okay, I know this didn't technically come out in this decade, but I'm still voting for it for the best customization in any Final Fantasy game that has come out sense. Bonus points for not having a whiny emo main character.
Racing Game of the Decade:
I always enjoyed Gran Turismo 4, so I'm putting this simply because it's the only one other than Ridge Racer I can think of right now.
Sports Game of the Decade:
Never played any that I enjoyed that much, so it's blank.
Also, no non-First Person shooters? Where am I suppose to flaunt my Touhou fanboyiness?