The Xbox 360 controller comes in both wired and wireless versions. Original Xbox controllers are not compatible with the Xbox 360. The controller is also compatible with PCs; the wireless version requires a Wireless Gaming Receiver in order to connect to the PC.
The wireless controllers run on either AA batteries or a rechargeable battery pack. The wired controllers may be connected to any of the USB ports on the console, or to an attached USB hub.
Source: Wikipedia, "Xbox 360 Controller", available under the CC-BY-SA License.