quote:
There are two methods of screw extraction when the screw heads are hopelessly damaged. The first is to just use an electric drill to remove the head of the screw. Drill directly through the center of the head with a drill bit maybe a third the size of the head, about 1/8" deep. Use progressively larger bits until the head of the screw comes off. Then, remove the maintenance panel. There should be more than enough screw shank (the "body" of the screw) remaining to grip with a pair of pliers... preferable self locking pliers such as Vicegrips. Hold tight and carefully turn the screw out.
If course, if the panel you are removing is very thin, there might not be enough screw shank to grip... so you can use a screw extractor instead. A screw extractor looks something like a blunt-ended screw with very broad threads. These hardened cutting threads are in the opposite direction of a standard right-hand threaded screw. When you turn the extractor, it tightens into the hole giving it a firm grip. To get a correctly sized screw extractor, take one of the screws you successfully removed to the hardware store. The salesman should be able to give you the correct size extractor and the right size drill bit for this job! The hole size is important... it should be no more than about 75% of the diameter of the screw shank. If you attempt to use too large an extractor by drilling too large a hole you may overly weaken the screw shank and the head might just break off! Back to step one!
Read more from Source:
http://www.stretcher.com/stories/990927j.cfm
How a screw extractor looks:
As mentioned in a previous post, you probably wont be able to find something like this in a small enough size but the first option mentioned in my quoted text (and suggested by Adeptus) could work.