An autonomous valet parking system was demonstrated last weekend by Volkswagen. A product of a partnership between Stanford University and the Volkswagen Automotive Innovation Laboratory (VAIL), a modified Passat can drive into a parking lot, find the first available space and neatly back up, parking the car autonomously.
(Volkswagen's autonomous valet parking demonstration video)
The system uses mostly off-the-shelf parts, including a front radar (already available as part of an adaptive cruise control system) a camera mounted in front of the rear view mirror (also available equipment on Passats) and LIDAR units mounted on the sides.
So why aren't you seeing cars happily backing themselves in while being taunted by parking valet union members? A slight hitch - the car cannot discern "obstacles" like human beings.
Interestingly, VAIL envisions special parking garages for cars that can autonomously park themselves. Once left at a drop-off area, the car would proceed to a "cars only" part of the garage.
Cars that park themselves have a curious history in science fiction. Cars that can drive themselves on special highways (like the Heinlein's Camden speedster were not smart enough to park themselves. SF writers much more commonly wrote about automated parking garages.
In his 1941 novel Methuselah's Children, Robert Heinlein wrote about an automated parking garage called a robopark:
Outside her friend's apartment [Mary] dropped down a bounce tube to the basement, claimed her car from the robopark, guided it up the ramp...
(Read more about Heinlein's robopark)
Frank Herbert briefly refers to a robotic parking garage in his 1977 novel The Dosadi Experiment and identifies a key element that makes it work - namely, grapple tracks.