Super Monkey Ball 1 and 2 are amazing, I think the second one especially is one of the best games SEGA ever made.
As for other SEGA stuff, Barry made a good list, though he forgot to mention how PSO has offline co-op splitscreen, Skies of Arcadia Legends has 15+ hours of new content (all great, too!) and I have no idea how he forgot about Beach Spikers! It even has Ulala in it FFS!
I assume you played the Sonic games already, but they are indeed the better releases out of the bunch. Xbox versions were fine, but had some minor control and speaker issues. Supposedly the surround sound on that version of Heroes is actually entirely reversed! Only Sonic Team.
Avoid Billy Hatcher and Amazing Island like the plague, but check out Virtua Quest if you can. I know the latter gets a lot of negative reactions, but it is really all not that bad outside of generic/lame character art. Near the end of the game it actually gets really cool too I thought!
There are tons of great non-SEGA games on GameCube as well, and while I put my full recommendation behind Donkey Kong Jungle Beat (amazing game), a fun fact is that the the creator of The House of the Dead series actually lead developement of all of the GameCube Donkey Kong games, so you should be required to get them regardless. 8-)
And because I know you love bizarre games, also check out:
Pikmin 1 and 2 - Brilliant and very hard RTS-like games.
Odama - Total War meets pinball action. I was not the biggest fan, but I think you will like it.
Cubivore - Action battle game with cube monsters!
Metal Arms: Glitch in the System - Overlooked game is overlooked.
Wario World - This game gets hate for some reason, but is a pretty cool beat em up. Also, it is made by Treasure, why argue?
Wave Race: Blue Storm - VERY SEGA-like series, I am sure you would love it.
Okay, the last three are not that weird. Try them all out anyways!
GameCube has dozens of other very good games, but to any would-be collectors, I strongly recommend picking them up sooner than later, GameCube prices are launching upwards fast.