Yes you can, although you will need an add-on for the Gamecube. The add-on attaches one the bottom of the cube, and you can buy it at most video-gaming stores (Gamestop).
There are hundreds of games: most N64 games have been ported, and there are some really great games. As far as I know, there is only one Pokemon game: Pokemon Colosseum. The gamecube can also play...