System: Nintendo 64
The Legacy: The single biggest console-to-console change in home gaming history was the Nintendo 64's controller: An M-Shaped contraption that looked like it was modeled after an alien bird, the N64 controller was just as notable for what it did have as for what it didn't. To start with the obvious: The analog stick, a full joystick that fit right over your thumb. The body of the controller? There were three different ways of holding it: With the D-Pad and the left-set buttons, with the analog stick and the left-set buttons, or with the analog stick and the D-Pad (which only a few games actually used).
As for those buttons? There were ten of them, one of which was the "trigger" idea introduced in the Virtual Boy. The game held the space for a memory pack, or a graphics expansion pack, or the rumble pack, the first time a "vibration" feature was introduced into a console system, which is now generally standard in all consoles. More than anything else? The thing just felt awesome in your hands. Of every Nintendo controller, the 64 set the standard for innovation, and was by far and away the most crucial step in the evolution of all the controllers to come.