Are there any Wii games that require me to use a Classic Controller and won't work with a Gamecube controller or Wiimote+Nunchuck? Are there any controllers that have both a Wiimote and a Gamecube plug so I don't have to buy two similar controllers?
No, there are no games that require a classic controller but do not work with either a gamecube controller or the wiimote & nunchuck combination.
There are games however that only support two out of the three combinations, most notably, Monster Hunter Tri, which only supports the classic controller and the wiimote+nunchuck combination, but do not support the Gamecube controller
Do note however that some games are not optimized for the gamecube controller and play a lot easier on the classic controller (SNES games notably) and the gamecube controller is the only controller that allows you to play gamecube games.
No. To the best of my knowledge, a Gamecube controller will work for all of the games that state that they require the classic controller; if you already own a Wavebird or Wired gamecube controller, you do not need to purchase the classic controller.
I don't think so either. But I'm pissy about MegaMan 9 and Samurai Shodown - they support classic but not GC controller. It was exactly these types of games I bought the GC controller for. On the other hand, Mario Kart and Smash Brothers and virtual console games all support GC controller, which I like.