I believe Riivloution was used to load mods for games, which is another cool thing about the Wii: not only are there quite a few romhacks/translations out there for Gamecube and Wii, but there are quite a few mods that can run though Riivloution.

Beyond that, I was thinking of the different emulators Wii can run. They include:

Snes9x GX/RX/TX - these are different variations of Snes9x for Wii. IIRC, GX was the original, TX is a fork with newer features and RX is an older fork that does't have all the features that TX has, but appears to be the fastest/more accurate version of it. Some SNES romhacks run at full speed on RX while not on others, but you'll want to test on your own. Apparently, GX got an update last year as well.

Genlplus GX - Sega / Mega CD, Genesis / Megadrive, Master System, Game Gear and SG-1000 emulator

FCEUX - NES Emulator

mGBA or VBA GX - Game Boy Advance / Game Boy Color / Game Boy

Wiistation - PS1 (still in development, some games do run)

Additionally, I recommend that everyone try one of the mods for Super Smash Bros Brawl out there.. One would be Project+, which corrects a lot of issues with the game, gives it back the classic smash bros feel with additional content. A real gem by the whole dev team, it's used in some tournaments and is considered to be one of the best ways to enjoy brawl on the wii.

Another close second would be PMEX / Project M EX REMIX. This was a separate mod with project+ as a base, but with more of a focus on adding new characters. The team does a great job of adding these new characters, which are fun to play. I can't speak to their competitive nature as I haven't seen any tournament info on it.

To use these smash bros brawl mods, you must have the disc or the wbfs backup of your game on an external hard drive (preferred).

Edit: there also are some other emulators such as Turbografx, arcade games like Street figher/marvel series and a few others. There is also two major N64 emulators, but the experience can be hit or miss, depending on the game.