It hasn't been mentioned nearly enough, but "Skies of Arcadia" needs to be on the list of must-haves for the gamecube. It's the best rpg made for the system, second one being "Tales of Symphonia", and well worth the investment to have.
"Paper Mario: Thousand Year Door" is also easy to find and fun to play, though they make it most rp'esk in gameplay, the writing for the game is satirical and witty.
You can get many of the "Spyro" games for next to nothing now, along with "Pikmin" (strategy) and the two "Harvest Moon" games (farming sim, buy at own discretion.)
The "Metal Gear Solid"s are worth owning, but it's already been brought up.
"Super Smash Bro's Melee" is a must have fighting game.
There is a "StarFox" game that looks deceivingly good, but I'd stay away from it. It's short and they rip out half of what a good StarFox game really is.
Edit - If I'm going to put quotations around one game, I may as well put quotations around them all.