I'll go first: I spent most of my gaming time with retro games, discovered the Duo, and played lots of other 16-bit and 8-bit games. But, other than that, here are the games I spent the most time with:
Under Defeat - I blew an entire spring break and then some with this game
Super Mario Galaxy 1 - Until this game out, my idea of a 3d platformer was a slow paced game where you had to annoyingly collect items and struggle with a busted camera
Super Mario Galaxy 2 - .. and this one added enemies

Super Monkey Ball - I was pretty obsessed with this one. Way better imo than its sequels.
Mars Matrix - This elevated my expectations of manic shmups quite a lot
Metroid Prime - The only Prime game I was into; I loved that they nailed the Metroid atmosphere perfectly (no small feat considering how screwed up so many 2d->3d attempts were). Few complaints about this one (mostly having to do with that damn elevator bug and some repeating enemy encounters).. maybe it could have had more action.
Ikaruga - Nothing to say about this that hasn't been said
F-Zero GX and AX (non-story mode, of course) - If you haven't played the arcade version yet, track it down
3d Grand Theft Autos - the missions bored me to death, but I loved just rampaging!
And.. a retrospective:
The last decade started with arcades on the decline but still a prominent part of the gaming landscape, and ended with arcades not really figuring into anything at all. During this time, Sega called it quits for hardware, Neo Geo was toast, Microsoft became a console maker, "shmups" entered the gaming lexicon (thanks Malc

On consoles, FPSses went from being a niche genre about demons and crap to being a hugely popular genre about patriotic bald soldier dudes. Independent games became very popular, which was a big shift from the previous Shareware scene. Online gaming also became feasible for the majority of players due to cheap broadband. Games on smartphones also became popular, and for once, millions of ordinary people were carrying electronic devices in their pocket capable of playing some pretty decent games.
I'm not sure if this changed gaming more than the 90s did, but it's fairly dramatic to look back and see what we take for granted now that didn't exist in 2000.