Wii Remote
The simplest alternative to the Classic Controller is the Wii Remote. Simply turn the Wii Remote on its side and use it like a standard controller. The Wii Remote's boxy feel is similar to that of an NES controller, so games like "Mega Man 9" can feel more authentic when using the Wii Remote. The biggest downside is that the Wii Remote only functions with some of the Virtual Console games. You cannot play Super Nintendo or Nintendo 64 games with the Wii Remote, and not all Mega Drive, Genesis or Neo Geo games will function with it either.
GameCube and WaveBird Controllers
Another alternative is the GameCube controller, which plugs into a port on top of the Wii. The GameCube controller works with almost all Virtual Console games, with only a few TurboGrafx-16 games being incompatible with it. The controller's design, however, makes playing some 2-D games more difficult, since the controller's directional pad is stiff and hard to use. Additionally, gamers who are used to wireless controllers may find it hard to go back to wired ones. Thus, you may want to purchase a Nintendo WaveBird controller. The WaveBird is a wireless controller made for the GameCube that functions by plugging a wireless signal device into the controller port. Nintendo has stopped producing WaveBirds, so you will likely have to visit eBay or the Amazon marketplace to find one.
Thrustmaster T-Wireless NW
Thrustmaster has released the T-Wireless NW, a wireless (and cheaper) alternative to the WaveBird. It also works by plugging a wireless signal device into the controller port. The controller also features a new design, closer in form to the PS2 controller.
Arcade Sticks
There are a handful of arcade-style joysticks available for the Wii, though they are a more expensive option. The Wii Fighting Stick by Hori was designed specifically for fighting games. It has a joystick and eight main face buttons. The Wii Neo Geo Stick 2 has a joystick, four main face buttons and four secondary face buttons. The Shaft by Overline Gaming uses six main face buttons and a joystick and is considerably smaller than the other two. Though the Shaft can be ordered direct from Overline Gaming, the other sticks are harder to find and are more expensive. Consult a specialty gaming store or look on eBay for more information about the Wii Fighting Stick and the Wii Neo Geo Stick 2.
Other Alternatives
Hori also produced a GameBoy Player Controller for use on the GameCube. It is similar in design to the Super Nintendo controller and was originally intended for use with the GameBoy player. It functions in the same way as a GameCube controller, albeit with a design more suited for classic games. The controller has been out of production for years, however, and it is difficult to find for a reasonable price.
Adapters like the Cube Joybox Pro by Mayflash allow you to plug a PS2 controller into a GameCube port. This would allow you to use a PS2 controller with Virtual Console games, though most of the adapters are hard to track down.