I bought a set of screw extractors from Sears for <$20 which sometimes work as a last resort. After liberally dousing the screw with penetrating oil and letting it sit the screw extractors will work a little more than 50% of the time. Still sometimes the head will break off and sometimes the screw doesn't budge, but you are no worse off than before.
Sail on silver girl. Sail on by. Your time has come to shine.