Whoever said Sonic Adventure DX, ignore them. The glitchiest, headache-inducing game I had the misfortune of playing. SA2:B, not as bad, but beware. Mega Collection and, to a lesser extent, Gems Collection are the best sonic for the 'cube.
Great ones no one mentioned:
Pikmin (haven't bothered with 2)
Soul Calibur II (Skraaa!)
Metroid Prime 1
Animal Crossing
EDIT: Thanks, Warprattler (not really.)
Eternal Darkness: sanity's Requiem
Metal Gear Solid: the twin snake
Both critically acclaimed(but poor-selling) games made by ex-second party developers Silicon Knights. I can't testify to them as I never played them, but I heard nothing but good.
Ikaruga, Published by Treasure. Another critically acclaimed game that flew under the radar. It's top-down shooter like Raiden.