GCEmu
GCEmu is a extremely incomplete emulator that was more designed as a proof of concept to show what is actually achievable.
Its aim was to show that emulation of the GameCube can be done at a reasonable speed with the right recompilation techniques and other tricks.
Development of GCEmu appeared to end sometime after its release in 2005.
We recommend a much more complete emulator for general usage, that emulator being Dolphin. This is more here for those who are interested in trying out some of the older generation of emulators and seeing how emulation of the GameCube improved over time.