Nintendo GameCube
IBM PowerPC, 486 MHz
ATI graphics
24+16 MB of RAM
8 cm optical drive
(optional) 10/100 Ethernet
Nintendo Wii
IBM PowerPC, 729 MHz
ARM SoC
ATI graphics
24+64 MB of RAM
12 cm optical drive
Wi-Fi
Bluetooth
USB
As they are "computers" with decent RAM and a good CPU, it makes sense to port Linux to these platforms.
Linux can be used:
to use a GameCube/Wii as a thin client
to use a GameCube/Wii as a multimedia terminal
to use a GameCube/Wii as a tiny PowerPC-based server
as a runtime environment for homebrew development
The GameCube Linux Project is in constant development. You are welcome to contribute!