If you already have a GC Pad then no you don't need to buy a new one. But if you don't have a GC pad then yes you will need to get one.
On a side note for those wondering, the Nintendo Wavebird controller works perfectly on the Wii too. No one wants wires these days...
If you already have one, there is a place on the Wii, dedicated to the Gamecube stuff. Just plug it in there. Either way, you NEED a Gamecube controller.
like i said before, its on the very top of the wii. put your hand on the edges of the top of the wii. pull up...one side will hinge...voila: game cube memory slots and controller plugin points.