I'd have to second Pikmin, Prince of Persia: Sands of Time, Metroid Prime, and Wind Waker as essentials on GC.
Tangent: And even though Pikmin 2 improved on Pikmin, I didn't care that much for the dungeon-crawling grottos after a while and I didn't even finish the game. Keeping the game above ground kept it more enjoyable imo, and kept the pikmin feel to it rather than the impending sense of doom I got after each time I descended and saw this wasn't the last level. It felt like it became more about the dungeons than exploration later in the game.
Anyhow, I think PoP is a must, and Wind Waker is great if you're familiar with Zelda (maybe play OoT first), Pikmin also because it's a unique kind of game, and Prime is great (but don't be surprised if you play it, then put it down for a year or so and then come back to finish it. Great game, but that happened with others too and it happened to me with both Prime 1 and 2. Worth pushing through/coming back to if that happens).