The Wii lets you use your internet connection to download games from a variety of legacy systems. This includes the N64, SNES, NES and Sega Genesis!
These games are not free. You pay for them with a credit card. There are also gift cards available, that you can buy at most gaming stores. This lets you give someone the gift of "points", which they can then use to buy games with.
Here's the list of available games on launch - November 19, 2006. The number shown after each game is the point cost.
donkey kong 500
mario bros 500
solomon's key 500
legend of zelda 500
wario's woods 500
super mario 64 1000
altered beat 800
sonic the hedgehog 800
You buy points at $10 increments, 1000 per $10. So 500 points is $5.
Wii Shop Channel Information
Playing GameCube Games on your Wii