Classic controller can be used with VC games, that you download from the Wii Shop Channel. You can also use a Gamecube controller for the Virtual Console titles if you wish to do so.
You can't play Fifa with the classic controller, you use the Wii remote and nunchuck. Plus the games have what controller types can be used with certain controllers on the back in the upper right corner. So when buying games in the future look on the back in the top right corner to see what you can use to play.
Games I know of that use the classic controller..Resident Evil 4, Mortal Kombat Armageddon, NiGHTS and the new Super Smash Bros. Brawl game which comes out Feb. 10th.