Can Wii play Gamecube games?

I haven't gotten a Wii yet, but I am dying to get one. I wanted to know if Wii will play gamecube games. I have a zelda collector's edition with a bunch of zelda games and was wondering If I could play that on a Wii.
Also, what are the chances of getting a Wii in California?
Update: Also do you need a memory card still, or did they put in some kind of a hard drive or memory storage in the game console?
11 answers 11