Emulators have been suggested, so I guess I should say something about Apps...

WiiMC - The ultimate Wii media center. Streaming? Check. Videos? Check. Music? Check. Images? Check. Must-have.
GeeXboX - Similar to the above, but based on Linux which is always a good thing. It is capable of running certain files, such as .mkv's much quicker than WiiMC, but has limited functionality and in my opinion "worse" GUI.
WiiEarth - Google Earth on the Wii = feel like you're in Minority Report and spy on your neighbours. Or just look for stuff.
WiiXplorer - Manage the content of your drives and the SD card without disconnecting them from the Wii. Handy.
WiiVNC - A VNC client for the Wii. Quite useful and very responsive.
Linux for Wii in various flavours - Duh!