'Sidewinder' is the colloquial name for the AIM-9, a supersonic infrared-homing air-to-air missile in use by air forces worldwide. The most current variant as of 2001, the AIM-9M, is manufactured by Raytheon; it is 9' long, 5" in diameter, weighs 190 pounds, and has a range of 10-18 miles. A single AIM-9M costs $84,000.
The AIM-9 project was begun in 1949 at the US Naval Weapons Center at China Lake in the Mojave Desert. Early versions of the missile - built on a shoestring budget, and restricted to a very small 5" diameter - only worked at very short ranges and tended to fishtail from side to side when in flight (hence the nickname.) It also tended to lock onto the sun or reflections from the ground, which had a detrimental effect on its effectiveness. Later versions eliminated this behavior, as well as improving the distance at which the missile could lock on to a target, its range and destructiveness, and gave it the ability to seek heat generated by friction on an aircraft's skin (eliminating the need for the attacking aircraft to be in view of the target's engines.)
Sidewinders were first used by the US Air Force in Vietnam. Great Britain's Royal Navy used them to great effect in the Falklands War in 1982, and 51 of the 55 Syrian MiGs destroyed in 1982 air battles with Israel were downed by Sidewinders. Coalition forces in the Gulf War destroyed 13 Iraqi aircraft with the missiles (although the number 12 has been reported, the 13th was downed by a pilot who meant to fire a radar-homing Sparrow but launched a Sidewinder by mistake.)
Thanks to f-16.net for the kill figures and the Sparrow/Sidewinder anecdote.