Screw Extractor Bit

A screw extractor (or screw remover set) is specifically designed for this problem. First, drill a small pilot hole into the center of the stripped screw head using a drill bit slightly smaller than the extractor. Then, insert the screw extractor bit into the hole (it has reverse threads). Using a drill (in reverse) or a tap wrench, turn the extractor counter-clockwise. The extractor's threads bite into the screw, allowing you to back it out.