I voted for Super Smash Brothers Melee. It was kind of difficult not to, since it is my most-played game on any system. SSBBrawl was a disaster.
The Legend of Zelda: Majora's Mask wasn't really something I liked. The structure of the game just bothered me, with all of the redundant tasks you were required to do.
Metroid Prime successfully combines the action of a first person shooter with exploration and discovery, and creates an incredible atmosphere. It's certainly one of the most well-crafted games I have ever seen.
Wii Sports could be arguably the most influential game of the decade, if you go by the sheer number of knockoffs out there.
Super Mario Galaxy is Super Mario Galaxy. Enough said.
I haven't played Resident Evil 4. Or any Resident Evil game for that matter.
There are plenty of games released over the last decade which I'd want to give special mention (ExciteBike 64, Banjo-Tooie, Battalion Wars, TimeSplitters, Mario Kart Wii, etc), but I'll mention just one that I feel really deserves some recognition: Perfect Dark.
Perfect Dark is still my favourite N64 game, so I quite disagree with anyone who states it is incompetent today. The controls are still excellent, the N64 controller works very well for FPS games with its layout and comfort, and the more resistant analogue stick makes aiming easier... but maybe this is more due to my own personal loathing of dual-analogue controllers. Its corridor levels are much better designed and make for better action than the open field levels in games like Halo, and its selection of weapons is staggering and includes pretty much any type you can think of.
The best feature of Perfect Dark is definitely the A.I. bots in the multiplayer mode. I know people will say that having online modes eliminates the need for bots, but I believe they're needed now more than ever. When you play online you are likely to find extremely skilled players who aren't even going to give you a chance; there's little hope of improving your skills if you're killed ten seconds after you respawn. Bots make for great practice because you can customize them to match your skill level, and even give them unique personality settings like moving really fast or slow, using only explosive weaponry, or having suicidal tendencies. Since I'm non-competitive my friends and I would never play the game against one another, but would instead always team up against the bots. It was a blast!