The Nintendo Wii accepts a variety of controllers, and controller options depending on the games and/or features being used.
Wiimote
As the name suggests, the controller looks and feels like a TV remote. It is a motion sensitive controller that can also be used as a pointing device (thanks to the included Sensor Bar). It can be used to perform pretty much any action from throwing a bowling ball, to pointing and shooting your weapons. The options are endless. It also includes the rumble feature we are so accustomed to as well as its own speaker. Other attachments can be connected to it through the expansion port.
Nunchuck
This is an attachment that not only has the analog stick we are used to playing with up till now, but also has the motion sensing technology used on the Wiimote. When used in conjunction with the Wiimote, game play is enhanced beyond my imagination through possible. It allows you to move around with the Nunchuck while performing daunting tasks with the Wiimote. The best part is that the player is not limited to a right handed set up. The controllers can be used on either hand for a more natural feel and experience.
Classic Controller
Not included with the console, this little beauty allows you to play the classic games purchased through the Virtual Console. Although many games can be played with the Wiimote or the Game Cube controllers, some require the Classic Controller. The controller is very similar to the Super NES controllers many of us remember.
This information and more can be obtained through the Nintendo Wii website.