i work at a hardware store...i gotta do this crap ALL the time..there are 2 good ways to do this...
as stated above, soak the screw with some good penetrant, i recommend B'laster
use a dremel to cut across the screw, and turn it into a flathead, make sure you use a big enough screwdriver to then turn it...
if all else fails, this works like a charm, buy a screw remover (preferably the smallest size if the screw is small) but BEWARE, DO NOT BUY ANY SCREW REMOVER WHICH LOOKS LIKE A BACKWARDS SCREW, they don't work worth shit....buy the screw remover which looks like a square with a point at the tip.
its square, but the edges are like knives and dig in absolutely wonderfully...heres how to do it
get a very very small drill pit and make your pilot hole in the middle of the screw, get a second larger drill big (smaller then the bit remover) and drill in, try to get as deep as you can (if your going in perfectly straight, you should have plenty of room)
then, take the bit remover and hammer it into the hole (do it straight!) hammer it in very well, you want it perfectly snug as this is your last chance to get it out without killing the hole.
use a tap holder, or carefully use a wrench and apply a perfectly perpendicular force, should snap out so easily you will be amazed that you couldn't get it out with a screwdriver.