Go to sears and get a eazyout.
Basically it's a tap but with reverse threads on it.
The idea is that you screw it into your nice rounded out hole (going counter clockwise), and then it grabs hold of the hold side and allows you to back out the screw.
They come with some drill bits too so you can make the hole bigger or deeper if need be.
Real nice for counter sunk screws.
For cap or button head screws, just get some vise grips, and crank them down so they're hard to lock. Then twist.