Hasn't been mentioned yet:
Rogue Squadron (OMG get this, liek naow!)
Prince of Persia (the first one is the best, or so I've heard)
Soul Calibur II
Viewtiful Joe 1/2 (if you like HARD games)
Maybe Burnout 2 (haven't played it, only played Burnout 3 and 4, but those games were amazing)
Possibly something from the Need For Speed series (Underground 2 or Most Wanted are probably the best) (if you like racing and can put up with cheesy FMV cutscenes and people talking about "street cred")
2nded:
Both Zelda games (Wind Waker and Twilight Princess)
Both Metroid games
Resident Evil 4
Eternal Darkness
Mario Kart Double Dash
Super Monkey Ball 2
I didn't like but YMMV:
F-Zero (story mode is totally impossible even on the easiest difficulty, otherwise decent)
Resident Evil 1/REmake (OMG horrible camera angles + controls, they significantly detract from the game)
Super Mario Sunshine (just didn't keep me interested and I kept getting stuck, though I may have liked it if I had stuck with it a little longer)