(Updated with Wii U)

NES
The Atari 2600 was king when the NES came to the scene. Controllers were either stiff joysticks with a single button or awkward paddles with hard-to-reach buttons. Both were easiest to use by holding them to the ground with one hand and controlling with the other. Nintendo changed all of this by allowing gamers to hold controller with both hands. It was so successful that "Nintendo Thumb" became a problem.

Innovations: D-pad, multiple buttons, microphone (Japan), light gun

SNES
The more ergonomic controller help to save thumbs, and shoulder buttons gave the index fingers something to do. The added front buttons helped to increase complexity in games.

Innovations: Shoulder buttons, ergonomic controller

N64
While awkward at first try, the N64 3-prong controller became an welcome evolution. For games that needed the new pseudo-analog thumbstick, players would hold in the middle and to the right; for games that needed the D-pad, players would hold on the left and right. The add-on slot allowed force feedback, tilt sensing, game saving, and more. Also it was the first console since the older Ataris to allow 4 controllers.

Innovations: Thumbstick, add-on slot, camera buttons, trigger button

GCN
This generation moved in the direction of true analog control for two thumbsticks and the shoulder buttons, allowing more immersion. Later in the generation, RF wireless was finally perfected, although not pioneered.

Innovations: Multiple analog thumbsticks, analog shoulder buttons with a hard digital click, usable RF wireless

Wii
When many gamers saw this wireless wand controller, or remote, in pictures online, they scratched their heads. Then they finally read about the remotes and found the accelerometer motion sensing and pointer aspects, that would replace many of the old analog controls of the previous generation. The Wii Remote senses 3 axis motion and positions and gravity. Additionally, it contains a 1.3Mpixel infrared digital camera to detect position with respect to an IR light source. The Nunchuk attachment senses 3 axis motion, using the expansion port of the Wii Remote. The Wii Motion Plus added gyroscopic motion sensing for more precision. None of these technologies were new independently, but they were ground-breaking when combined into on interface.

Innovations: accelerometer and gyroscopic motion sensing, accelerometer and gyroscopic position sensing, BlueTooth wireless, IR pointer

Wii U
The Wii U adds a modernized dumb terminal that communicates over a custom WiFi protocol. This terminal, the GamePad, takes all the button configurations of the previous generation, moves the Sensor Bar onto itself (for Wii Remote pointing), and adds a camera and 480p widescreen touchscreen. By using a terminal configuration, it is possible to play games when the television is powered off. Though the Wii U supports 2 GamePads at once, this feature has not yet been implemented.

Innovations: Dumb terminal controller, asymmetric gameplay, video chat without peripherals, off-screen play