Half-Life 2 (2004)
I just beat this game for the first time, and despite the first hour or so still not drawing me in, it was a fantastic game. Despite knowing it was linear as hell I kept thinking to myself "Man, this world is huge and so detailed." Vale successfully kept everything I didn't need to see hidden in a non-obvious way, and I kept getting sucked into the level design. Also, since I've played through it so late I was touched by the things like health packs, shields, and carrying nine weapons and tons of ammo with no problem. Nostalgia for older shooters certainly made me smile more than once. While I loathe the first-person platforming segments, the game still only let me stop playing after several hours per session. The segments with squads of humans or antlions under your control also helped break up the monotony in creative and well-executed ways. The scripting of events was perfect and kept me on my toes, and more then once startled the crap out of me. Finally, Ravenholm.

Thief II: The Metal Age (2000)
A good example of a sequel improving on the raw ideas of it's predecessor, Thief II was better in just about every way. It mostly got rid of the creatures in the first, replacing the missions with more open levels surrounding humans and their robotic buddies. The stealth was refined to greatness, the improved AI behaviors worked great, and the gameplay allowed for much experimentation. This is hands-down still my favorite stealth game ever.

Call of Duty (2003)/CoD: United Offensive (2004)
Call of Duty was simply amazing for me when I played it the first time. The massive battles, tightly scripted sequences, and soaring score worked fantastic together, making this game the equivalent of a Micheal Bay movie. The wealth of weapons offered by the three separate campaigns were well-balanced and fun as well, especially for the multiplayer. The first two Russian levels were also amazing. The expansion, while lacking some of the grandness of the first, improved on the gameplay enough to really standout as well. This is also the first game I played extensively online, so it holds a special place in my heart.

Dragon Quest VIII (2005)
Pretty much what Bolivar said. The beautiful graphics, charming characters, fantastical settings, and superb gameplay really drew me in when I play it this past summer. Definitely made me look into the series and pine for good JRPG's.

Shadow of the Colossus (2005)
Epic. The feeling, the vastness of the world, the music, the titular colossi. This game grabbed me when I first saw it being played, and playing it was simply breathtaking. The different colossi really made me think about how to beat them, and felt incredible to climb all over. I believe it is the 13th colossus (the flying snake in the desert) that just made me feel like a freaking badass taking it down. The story being conveyed mostly by subtleties also was a breath of fresh air.

Portal (2007)
Glados and the gameplay mechanic, along with the typical way Valve tells story through small things in a game, really sold me on this. Also, it hurt my brain in a good way at times)

These are the only five I can think of that really wowed me this decade. There were plenty of games that I loved that I don't include in this list (Resident Evil 4, God of War, Metal Gear Solid 3, The Elder Scrolls IV: Oblivion, Professor Layton), but if I had to chose one for the whole decade it would be one of the above. If looking at the entire landscape of gaming I would probably have to put Half-Life 2 up there as the game of the decade, but for the time I played it still think Thief II affected me the most.

Best Decade?
Even doing my best to remove the nostalgia googles, I still feel that the 90's were a better year for gaming as a whole. The refinement or creation of genres was astounding, to say nothing of the advent of 3D. While there was a lot of crap then also, I think at the time we saw them as no worse then we see the myriad of mediocre/crappy games from this decade. I also feel the 90's were fully of crazy experimentation, and while oftentimes not utilized properly that spirit of trying has since slowly become absent in most aspects of gaming for this decade. While I love tons of games from the past ten years, it still doesn't quite compare for me.