Joysticks were originally used in helicopters and other modes of aviation. When flight simulators were developed, joysticks naturally went along for the ride to make the simulation more realistic. Since then, joysticks have become the most popular form of game controllers for arcade games as well as home video game consoles.
Digital Joysticks
Digital joysticks are the most common joysticks used for PCs, employing simple left, right, up, down and firing commands. They are also called "Atari-style" digital joysticks, since they were first implemented with the Atari 2600 video game system.
Paddle Joysticks
Paddle joysticks consist of one knob used to control the game and one firing button. This is one of the oldest joysticks, as it was first introduced with the very first home video game consoles.
Analog Joysticks
Analog joysticks combine both concepts presented in the digital and paddle joysticks; they control the game like a digital joystick, but also use potentiometers to measure the movements like the paddle joysticks.
PC Analog Joysticks
IBM first presented this joystick with their personal computer. It's a simple analog-styled joystick with multiple buttons that usually connects via an USB port.
Joypads
Joypads are joysticks without the sticks. Instead, they employ a directional pad (D-pad) to control the game. Joypads are considered a bit primitive, but they are still featured among the current video game controllers.