Metal Gear Solid:Twin Snakes
Sonic Adventure 2 Battle
Time Splitters 2
You have SSX 3 on your list, I highly recommend SSX Tricky. It's the best IMO.(Although 3 is a close second)
Not sure if its a must have, but Baten Kaitos deserves a mention.
SSX Trick is better on the PS2, though I say this going almost entirely on reviews. I've only played it on the PS2, but I can see that if they just did a straight port without thinking about how to change the control scheme for the Gamecube (which they apparently didn't for Tricky - they supposedly did a better job with the later games), then it would be less than ideal on the Cube.
Note that The Legend of Zelda Four Swords is not going to be quite the same when played on the Wii since it isn't possible to hook up GBAs to the Wii. I have no direct experience with the game (again), but my older son and his cousin and a friend are having a blast with this game, but playing on a GC and with 3 GBAs hooked up. It doesn't seem like it would be the same without the GBAs.
I do have direct experience with Ikaruga. It's a solid game and has some unique aspects, but it is a shooter, so whether or not you should pick that up depends on whether or not you like shooters. I had the game for a little while and enjoyed it, but then decided that I'd rather sell it for a profit and pick it up again later, going on the presumption that the Xbox 360 download release of the game would lower the price of the GC version. I haven't checked lately to see if that has actually happened, though. At some point I definitely want to get it again regardless.
Donkey Konga is fantastic. I also have Donkey Konga 2 but haven't opened it yet. It's not suppose be as good as the original, but the original is fantastic and definitely should be on your list if you like rhythm games. I'm probably in the minority on it, though, in that I don't really like to play Donkey Konga multiplayer, because the mics (there to pick up claps) pick up other players all the time. No amount of playing with the sensitivity really solves the problem. I find that frustrating. However, it's a really fun single-player game too. I've also got Donkey Kong Jungle Beat but also unopened (I'm planning to give it to my kids this xmas.)