It's a tough call, really. I'm gonna break it down (loosely) by genre:
FPS: Half-Life 2 seems like a shoe-in, if only so I don't lose my gamer cred. I had more fun with ODST (and have an unhealthy appreciation for anything Nathan Fillion is associated with), but in terms of actually moving the industry forward, I've gotta give this to Valve.
RTS: It has to be one of the Total War series of games. I liked Rome, but I'm actually gonna throw it back to Medieval, Total War. Something about Risk + RTS appeals to the world-conqueror to me. Plus, I could actually beat Medieval, and always got stuck in Rome with maxed out popularity and an army which could block out the sun. The game got Nintendo hard, and just started throwing more and more enemies and rebellions at me.
Western RPG: Bioware wins it for me either way, but it's a tough choice between Mass Effect and Knights of the Old Republic. Both have their upsides and downsides. But, with Bioware still working on Mass Effect sequels, the promise of resolution to the loose ends (something now seemingly impossible for the KOTOR games) puts it higher in my estimations.
JRPG: Obviously, FFX and FFXII have to be considered. TWEWY, Fire Emblem (any of them, really), the new Pokemon games, and many others all had to be in the running. But, I'm giving it up for Persona 4. Brilliantly written (and translated), surprisingly atmospheric, beautiful voice acting, and some of the best music I've ever heard in a video game. I can save my overwhelming fanboyism for another thread (which I'll be creating shortly), but it's just fantastic.
Puzzle/adventure: I'm making this kind of a catchall category for those games which are primarily puzzle-solving, platforming, or otherwise in the pigeon-hole of action/adventure". It may be considered unfair to pit the new Monkey Island games against Portal, but it's the only way I thought to categorize them. Portal is, at its heart, a puzzle game. Not so much of the "find object x for door y" type, but it's still puzzles. As such, I'm giving the category to Portal.
MMORPG: Given that I'm currently playing WoW (though not obsessively, I promise), I'm tempted to just go with one of the expansion packs. The Old Republic is still TBA, so I'm actually kind of at a loss for this category. And suggestions would be helpful.
If I missed any categories, I apologize. But, for the top game:
I'm an RPG enthusiast, so it's largely down to Mass Effect and Persona 4. I liked them both a lot, and for many of the same reasons. Still, I have to give it to P4. Not just because it's a JRPG (and I tend to actually prefer turn-based combat). The story is a bit more involved, and there's a lot more development of the secondary and side characters. But, the big reason is this: it subverts the big trope of the player-controlled protagonist: the malleability of his character. Usually, I rail on about the fact that the game allows you to change personalities at the drop of a hat, but Persona actually expects you to. I can go into depth in a companion post about why Persona 4 rocks my socks.