Nintendo has its own graphics API (GX) for the Wii, which is resemblant of OpenGL but still different enough that some work is required to get OpenGL running. A way to handle this though is by having a Mesa driver translate the OpenGL calls into the Wii's GX API. This is similar to gl2gx, which is an open-source project that serves as a software wrapper for the Nintendo Wii and GameCube.
Their first OpenGL instructions running on the Nintendo Wii is shown below (it's not much, but at least it's better than seeing glxgears).
To follow the ongoing discussions taking place about Mesa for the Nintendo Wii, read this mailing list thread.