Dolwin is the first ever GameCube emulator to be publicly released. it is open source and written in C. However sadly development stalled in 2005 and not a single new release has been seen since. This could be partly due to the success of the Game Cube and Wii emulator, Dolphin.
Before development ceasing, the emulator did manage to boot and even run some commercial games and a few demos. However for the most part the emulator is fairly incomplete and should not be expected to run any games perfectly or even be able to boot them.
If you are are after the best emulator for the GameCube, see Dolphin.