One game that not everyone appreciates, but which we find to be really fun is Kirby Airride. You have to get use to the visuals in the main race modes, but once you do the races are super fun, with lots of abilities to pick up, switches to switch to do things to the track, etc, and that mode is only part of the game. The City Trial mode is fantastic and lately we've been getting into Top Ride, a top-down view race. There's also lots of options to play with to change each mode of the game around. Really cool, and underrated game IMHO.
Oh, and another thing to do with a cheap gamecube is get a second one and also pick up a couple broadband adapters to play Kirby Airride, Mario Kart and 1080 Avalanche in network mode. Of course you also need another TV! In theory you can hook up to 8 gamecubes together for Mario Kart. We don't have 1080 Avalanche, but we've played Kirby and Mario Kart this way. Mario Kart allows up to 8 player races (up to 4 players per screen/GC), balloon and shine battles (but curiously, and sadly, no bob-bomb blast mode? Sadness .( Kirby just lets you spread the players out over the screens, so with two GCs and two screens each player gets half a screen instead of only 1/4, but that does make a difference, especially for the main races (see note above about the crazy visuals - Kirby's main races look much better, and are easier to play, on half or all of a screen.)