The Classic Controller is an accessory for the Wii, which allows players to use a more old-school type of controller, with joysticks and L and R shoulder buttons. It can be plugged into the Wii Remote outlet on the bottom, and from there, players can control whatever game they are playing with the Classic Controller alone (unlike the Nunchuk which works side by side with the Remote.)
Mario Kart Wii, a Wii game that allows pretty much all controller options, lets players utilize the Classic Controller.
The earliest model of the Classic Controller is an almost flat circle with two parallel sides (sort of like a "0"). The left side has a D-pad, and on the south are two side by side joysticks; the left joystick is usually the only one used in gameplay, but several games implement the right. The Home Button is flanked by the + and - buttons on either side, right in the center. A, B, X, and Y buttons are on the opposite side as the D-pad, and the A and B buttons are translucent (importante!).The top of the Classic Controller has two classic L and R buttons, two circular buttons right next to them marked LD and RD, respectively, that do nothing, and a center button that opens up a small port on the backside of the controller, presumably to cool it down, although nobody really knows what it's for. All that, and then a wire is attached to the top with a plug-in to fit into Wii Remotes.
The A and B buttons control the Acceleration and braking in Mario Kart Wii, and the left joystick handles the steering. Due to the Classic Controller not having motion detection, pressing the D-pad lets players perform tricks... L and R deal with Items and Drifting...that's about it.
Like the Nunchuk, it was produced in a few different colors, including white (standard), black, and even golden.
Several upgrades have been made to the Classic Controller, including two lower handles for a better grip (this version is pretty popular, 'cause its even more classy, and plus, nice grips). The Wii U introduced the Classic Controller Pro, which has a similar appearance to the one with handles (some don't even have wires!), and has added upgrades.
Prices for standard and updated Classic Controllers are around $20 bucks, and Wii U version are actually cheaper, at $14.99.