The Nintendo 64 controller is the standard game controller included with the Nintendo 64. Released by Nintendo in late 1996 in Japan and North America, and 1997 in Europe, it features ten buttons, one digital (not analog) control stick and a directional pad, all laid out in a "M" shape.
The controller for the Nintendo 64 was designed to be held in several different positions. It was designed around Super Mario 64. It could be held by the two outer grips, allowing use of the digital D-pad, right-hand face buttons and the "L" and "R" shoulder buttons (but not the "Z" trigger or analog stick). It could be also held by the center and right-hand grip, allowing the use of the single control stick, the right hand-buttons, the "R" shoulder button, and the "Z" trigger on the rear (but not the "L" shoulder button or D-pad). More often than not the analog stick was used in games while in some, both the control stick and directional pad could be interchangeable (ex: Mortal Kombat Trilogy). Very few games used the directional pad exclusively; two examples are the 3D puzzle game Tetrisphere and the side-scrolling platformer Kirby 64: The Crystal Shards.
The controller also included four "C buttons", which were originally intended to control the camera in the N64's three dimensional environments. However, since the pad only contained three other face buttons, the C-buttons often became assigned to ulterior functions. An example of this is The Legend of Zelda: Ocarina of Time, where the C-buttons can be assigned to secondary items and the "Z"-trigger is used to orient the camera.
European controllers have a special Ferrite core about 4 centimeters from the connector plug, to prevent the user from being shocked by the power being supplied to it by the system if the wires become exposed. It also acts as cable tensioner.
One game, Robotron 64, allowed one player to use two controllers to control an avatar. This way the game played like its predecessor, Robotron 2084. Star Wars Episode 1: Racer, GoldenEye 007 and Perfect Dark also used this set up for slightly different gameplay experiences (in terms of control, at least) compared to the standard single controller option.
The controller initially came in six colors (grey, black, red, green, yellow and blue) but other colors were released later, many of them coinciding with the release of a similarly color or designed system. Some of these others include: smoke black, watermelon red, jungle green, fire orange, ice blue, grape purple, and special edition colors like gold, atomic purple, extreme green, "Donkey Kong 64" banana bunch yellow, "Pokémon" blue/yellow and "Millenium 2000" platinum.
For many years, console designers and manufacturers ignored analog stick technology, instead preferring the digital D-pad. It was not until the emergence of 3D gameplay that the analog stick was put into widespread use. Using a D-pad in a 3D game greatly limits the players ability to accurately utilize 360° of motion. Some early 3D games like Resident Evil overcame this limitation by assigning the Left and Right directions on the D-pad to spin the character rather than make the character move in that direction.
However, with the prevalence of analog sticks, the aforementioned D-pad limitation was no longer an issue. Though the Nintendo 64 wasn't the first console to use an analog stick (the Vectrex was first), it did popularize the idea. Its release followed Sega's analog Mission Stick for Sega Saturn as well as Sony's Analog Joystick and was followed during the fifth generation by Sony's Dual Analog and Dual Shock controllers for the PlayStation system as well as Sega's 3D control pad for their Saturn system and the analog controller for their Dreamcast system.
The analog stick was prone to some long-term reliability issues. If used excessively, the stick became "loose", which means it will not fully return to center position, which may render gameplay more difficult by giving unintended, non-user input to the system. This loosening can be caused by rotating it intensively - a common practice in games like Mario Party where it offers an advantage for some mini-games. Excessive rotating of the analog stick even resulted in blisters and burns to the hands, and Nintendo offered protective gloves to prevent injuries.
The original Rumble Pak, designed for the Nintendo 64 controller, was released in April 1997 to coincide with the release of Star Fox 64 and required two AAA batteries. Its specific use was to provide haptic feedback during gameplay; an effort to make the gaming experience more engaging. It was designed to be inserted into the controller's memory cartridge slot, which prevented the use of the Controller Pak. This usually had little impact, as Nintendo 64 games were cartridge based and had the ability to store saved data in the cartridge itself. This was also true because the insertion of a controller Pak was prompted at every point of save in case the before said Pak was not already in place.
Source: Wikipedia, "Nintendo 64 controller", available under the CC-BY-SA License.