NES, SNES emulation on the Wii

If you haven't tried it, do it. It's the easiest way to play your old games ever. You'll need to install the Homebrew Channel, which is pretty simple to do as long as you have an SD Card and haven't updated your Wii's firmware since June 21, 2010 or later. A Classic or GameCube controller for your Wii is a must for systems like the SNES with more buttons.

You'll need Bannerbomb:
http://wiibrew.org/wiki/Bannerbomb

And some homebrew to run:
http://wiibrew.org/wiki/Main_Page

There are ports of Snes9x and FCE Ultra, IMO a couple of the best emulators available, as well as emulators for all other mainstream systems from back in the day. Keep in mind that updating your Wii's firmware will remove the Homebrew Channel as this is unauthorized by Nintendo. You may also not be able to play brand new games or access some online features (Wii Store) without additional modifications or upgrades that may make the Homebrew Channel unusable. Any questions, ask.