Metroid Prime and Resident Evil 4. Both fantastic evolutions in their respective franchises.

Metroid Prime managed to not only recreate the Metroid feel in 3D but using a first person perspective. The exploration is engrossing, the boss fights are spectacular and it's a pleasure to hunt for new abilities and power ups.

Resident Evil 4 updated a series that was getting stale, just by the intro you knew you were in for quite a ride. Having the villagers hunting you throughout the streets, up the stairs and the rooftops was exhilarating. The game is wonderfully paced, each location not overstaying its welcome, each new area bringing new challenges, the story was camp but enjoyable and Leon kicks ass.

Resident Evil 4 and Final Fantasy XII to me.

Also, Modern Warfare.

If we're just going by what I think is the best game of the decade, then it's Final Fantasy IX without question. After that comes Valkyria Chronicles, Shadow of the Colossus, MGS3 and Final Fantasy X.

Most influential game is something completely different, and that would probably go to either GTA III, Modern Warfare, or World of Warcraft.

Freedom Force is my personal favorite game of that decade.  I enjoyed the hell out it when I first played it.  It broke the "curse of the superhero game" that people don't even remember anymore, because there have been a ton of great superhero games since.  Most importantly the only other game remotely like it is the sequel, although I think the first game is better.  It's a really fun and amazing, one of a kind game.

If I were to pick most influential that is not necessarily my favorite it would probably be Wii Sports.  Minecraft is also a good contender, but it was released at the end of the decade and grew in popularity gradually, so it is more associated with the current decade.  Wii Sports basically defined the whole decade and generation 7 though.  It caused a major cultural phenomenon and even Sony and Microsoft had their own motion controls after a few years.

If I were to pick a game I really liked and was really popular it would be New Super Mario Bros Wii.  My family played that game for 500+ hours.  It was the first time I experienced multi-player 2D Mario.  And the Wii set a December sales record in the US the month after it was released.  It's such an awesome game in every way.

My personal picks would be Uncharted 2, FFXII and Suikoden V. And to a lesser extent Shadow of the Colossus, DQVIII, Mario Galaxy and The Legend of Zelda: Twilight Princess.
I enjoyed the hell out of each one of them and for me at least they meant much more than some other "influential" games of the time.

I'll go with the most influential games of that decade IMO (no particular order):

- WoW
- GTA III
- Half-life 2
- Sims
- Wii Sports
- Halo
- CoD4

I'd put wii sporta up there for the reason of removing the anti social reputation gaming had before that, wii sports as flawed as it is made gaming cool

GTA3 as it had the biggest impact on the industry.

ZOE2

My Top 5 in no particular order:

Counter Strike
Half Life 2
Elder Scrolls
Animal Crossing
Portal