If you have a Dremel, grind a slot into it and unscrew it.
This has saved my ass many times. I keep one of those diamond coated wheels on a spare cutoff mandrel already mounted up pretty much specifically for this purpose.
Harbor Freight has a pretty cheap left handed drill bit set that is sometimes a lifesaver in these situations. Many times I just start drilling it with the left hand bit and often the bit grabs and unscrews the screw before even getting to the phase of trying the screw extractor on it. Sometimes not.