Best way to remove rounded off screws?

[K1RC]

We've all done it and its a pain What's the best way to remove one? Usually I would dremel across the top and unscrew with a flat head screwdriver to remove my hex head screws, however the latest one I did was set deep inside a part and I couldn't do this. So what's the best way to get one of them out? Drilling? How's best to go about that without damaging other parts too much? Thanks in advanced