A game controller is a specialized input device optimized for use with games. Unlike mice and trackballs, which are relatively standardized in form and function, game controllers run the gamut in shape, size, features, and purpose. Some game controllers sit on the desktop. Others clamp to the desk, and still others are held in both hands and manipulated directly. Game controllers may have a joystick, a steering wheel, a flight yoke, or foot pedals, or may be what we call "grab, twist, and squeeze" controllers.
A particular game controller may be well-suited for one game and entirely inappropriate for another. For example, a game controller with a steering wheel may be perfect for playing NASCAR Winston Cup Racing, but unusable for a first-person shooter (FPS) game such as Quake. Serious gamers who play diverse games often own several game controllers and use the one most appropriate for the game they are playing at the moment.
Game controllers attach either to a game port, which most sound adapters provide as a combined game/MIDI port, or to a USB port. Although you may have only one game/MIDI port on a PC, that port can support two game controllers simultaneously by using a splitter, which is supplied with many game controllers or can be purchased at most computer stores. Also, some game controllers have ports on the controller itself, which allow additional controllers to be daisy-chained from the controller attached to the PC. As you might expect, it's possible to connect multiple USB game controllers, although not all combinations work properly and conflicts are common.