This was supposed to be the GameCube's equivalent of Super Mario 64, but obviously things didn't pan out that way. Despite mixed reception, the game became commercially successful, found a devoted fanbase, and apparently warrants a sequel on 3DS (which isn't out yet as of this writing).
Mario Kart Double Dash. It didn't revolutionize the Mario Kart franchise like many hoped it would, but the improvements here go beyond surface deep. The character and vehicle selection is huge, the new weapons are appropriately insane complements to returning classics, and the tracks themselves have never been this diverse.
Mario Kart: Double Dash!! (Nintendo GameCube, 2003)
Wario World (Nintendo), GameCube; platform game developed by Treasure. It marks Wario's first starring appearance on a home game console. The game's plot centers around Wario & his quest to regain his treasure & his castle from Black Jewel, an evil gem. Wario World's gameplay centers mainly on combating enemies, although it requires some platform navigation similar to Super Mario 64 & Super Mario Sunshine. Sold over 142k copies in Japan - yet critical reception was fair to middling.
Pikmin is a really unique and super fun series of games. The idea lends itself to so many fun possibilities for puzzle, strategy, and all sorts of crazy fun mishaps. The games capitalize on all of these things very well.