Right now I have:
Metal Gear Solid - Twin Snakes (Play it and realise what platform this *should've* been on!)
Starfox Adventures (looks kiddie but trust me lots of fun!)
Pikmin 1 & 2 (strangely addictive as lemmings)
Bill Hatcher and the Giant Egg (see starfox desc.)
Need for Speed 1 & 2 (Good games on any platform, but framerate issues on Most Wanted and Carbon.. then again I have those on the 360)
Resident Evil 0-4, plus Veronica X (4 is a must buy, 0 has the best storyline in the classic series style)
Final Fantasy - Crystal Chronicles (bloody AWESOME!)
Pokemon Colloseum & XD (only XD is worthwhile)
Viewtiful Joe 1 & 2 (fun)
Metroid Prime & Echos (bizarre first person take on the platformer game)
Phantasy Star Online 1, 2 & 3 (very popular on/offline rpgs)
Tales of Symphonia (best japanese style rpg on the GC)
Mario Sunshine & Extreme Football (Sunshine is a great addition to the Mario series)
Super Smash Bros Melee
Baulder's Gate Dark Alliance
Harvest Moon
Animal Crossing (too addictive, reschedual life around game!)
Zelda Windwaker, Twilight Princess, and Collectors Edition
Splinter Cell (although better on the Xbox)
Trapt, Stolen and Rogue Ops (while all different games, they're basically the same thing.. female, 3rd person shooters. they're all quite fun, but suffer from control issues)
Prince of Persia 1, 2 & 3 (better on the PS2 imo)
I'm sure we have more but I totally forget what right now.