My GameCube collection is quite small and of what I have not all are great.
My three top picks:
Animal Crossing probably got the most playtime and was my first game for the system. But with the DS one out and probably a Wii one coming it's up to you. The GC completely burned me out on the DS one making it far less enjoyable than someone who went into it fresh.
Wind Waker is a must-have IMO. One of the most beautiful and fun games out there. People complain about the so-called "collect-a-thon" and many seem to never finish, but I went through twice and loved it both times. And my third game I absolutely love is
F-Zero GX. It's perfect. I cannot think of any way to improve upon the game other than perhaps online and a track editor. Mighty Typhoon FTW!
Others:
Metroid Prime: I love the exploring and puzzle aspects but was personally turned off by the fighting. I never finished it.
Sonic Mega Collection: All Genesis Sonics. It was something I needed. My Genesis brought I was a huge Sonic fan. Oh how Sega destroyed my beloved hedgehog in these modern times.
Ikaruga: Quite fun. Drove me insane trying to combo through all the levels rather that mindlessly killing everything.
Viewtiful Joe: Also quite good. Um, yeah...nice game.
Mario Kart Doube Dash: Another game people complained about. It was my most played game with my roommates at college. Heads and tails over previous versions IMO. Although switching behind playing that and MKDS severely messed me up with the controling so different.
Pikmin 2: I wished I played more of this. My cube went into retirement after I transfered colleges and no longer have a tv to play my cube one. I bought it right before this. Once I get my Wii this shall be the first cube game I go back to.