Yes

FROM:
http://en.wikipedia.org/wiki/Wii

Backward compatibility
Nintendo GameCube ports on the top of the Wii unit

The Wii console is backward compatible with all official Nintendo GameCube software, as well as Nintendo GameCube Memory Cards and controllers. Compatibility with software is achieved with the slot-loading drive's ability to accept Nintendo GameCube Game Discs. The console supports progressive-scan output in 480p-enabled GameCube titles. Peripherals can be connected via a set of four GameCube controller ports and two Memory Card slots concealed by removable flip-open panels.[2] The console therefore retains connectivity with the Game Boy Advance and e-Reader through the Game Boy Advance Cable, which is used in the same manner as it was used with the GameCube. This feature can only be accessed on those select GameCube titles that previously utilized it. Gamercize accessories also utilize the backward compatibility in order to support the Wii console. The Wii for release in South Korea lacks GameCube backward compatibility.[105]

A Wii console running a GameCube disc is restricted to GameCube functionality. As such, a GameCube controller is required to play GameCube titles, as neither the Wii Remote nor the Classic Controller functions in this capacity. A Nintendo GameCube Memory Card is also necessary to save game progress and content, as the Wii internal flash memory will not save GameCube games.

Backward compatibility is limited in some areas. Online and LAN-enabled features for Nintendo GameCube titles are unavailable on the Wii, as the console lacks serial ports for the Broadband Adapter and Modem Adapter. The console uses a proprietary port for video output and is therefore incompatible with all Nintendo GameCube audio/video cables (composite video, S-Video, component video and RGB SCART). The console also lacks the GameCube footprint and high-speed port needed for Game Boy Player support. The Wii was initially compatible with the GameCube Action Replay, which would work with GameCube titles. The firmware update to 3.0 has caused restrictions to this device along with various unlicensed freeloaders, however.[106]

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