@Drakusatheon: Sorry, you are wrong. Wrong. Wrong. Wrong.
Super Mario Sunshine, while nowhere near the best Mario game, is one of the best games of the console. The entire game took a fun concept, as far as I know only used extensively on PC, and made it genuinely unique. The game was colorful, challenging and most of all, Mario.
The best underrated game of both this, and last generation is gotta be Eternal Darkness, and I'm going mad trying to figure out why nobody has mentioned it.
It is, without a doubt, the only game that has truly scared me beyond the cheap Wall Demon scares of most games Survival Horrors.
The story is magnificent, the characters show some really decent emotion and the way they tie together is relatively well done. The combat is pretty good, but the magic is where the game really shines.
This is my list of games you should buy, with the exception of MP, I'll add different games because you should pick up every game everyone else suggested.
Metroid Prime -This is my favorite console game.
Eternal Darkness
Mario Kart Double Dash!!
F-Zero GX
MGS Twin Snakes
Super Monkey Ball 2
Ikaruga
Oh, definitely pick up Skies of Arcadia. Never played the GC version, but I was all over the DC version.