Geist - awesome puzzles, first person action/adventure, good storyline and great gameplay.
Resident Evil 4 - only played the PS2 version, but I'm sure the Cube version is just as good.. but with less extras/stuff.
Fire Emblem: Path of Radiance - strategy game, just as great as the handheld version, deep story, a large great cast.
Metroid Prime - another first person action/adventure, one of the best 2D to 3D transitions. EVAR.
Legend of Zelda: Four Swords Adventure - fun Zelda game with puzzles-a-plenty, level based format, traditional Zelda gameplay, 2D rules all, etc., etc.
LoZ: Twilight Princess - one of the best LoZ titles EVER. Then again, that's coming from someone who thought LttP and OoT were the best.
That's just about all the best titles I've played on the Cube.. the ones that stood out the most. Other recommendations include Super Smash Bros. Melee, the Star Fox titles (they were mediocre, but still good) and Mario Kart DD!! (new spin on MK gaming, but still fun, as ever).