As sure as black cats have black kittens, sooner or later you will strip the head of a screw. hopefully you will have a Trend Grabit around. It's got a reverse cutting drill bit to drill out a hole in the screw, and a reverse threaded cone to dig into the hole and unscrew the screw.
One thing to bear in mind. You do have to drill out a hole in the top of the screw, even thought the screw may appear nicely drilled by your previous attempts to screw it in, the hole that the grabit makes is the correct shape for the threaded cone to grab.
There's a series of pictures here http://www.trendmachinery.co.uk/grabit/