Penetrating oil, vibration, and in extreme cases, heat. If a screw has to come out, it has to come out, and I always approach stubborn screws by starting off gently and then slowly escalating to more severe techniques if required. However, the first approach should always be to use the proper tool - it has to fit perfectly - and ones with long shafts to give you more torque. If that doesn't work, then move on to a good penetrating oil. Worst case scenarios involve drilling the screw out, but I'd advise practicing that technique on something less important if you've never done it before.

I'll second thetypewriterman's tip. Using vibration is the handyman's secret weapon (I've heard that line before somewhere?) On a stubborn screw I'll soak in gun oil or penetrating oil overnight (penetrating oil stinks like kerosene and I'll only use it in my garage) and then I'll start by gently rapping with something small and metal, like a crescent wrench or a bigger closed end wrench. Then I'll put the engineering screwdriver (I only own one of them but I'm keeping my eyes open at yard and garage sales for more of them) on it and arrange my body into a contorted form so I can put heavy turning pressure on the screwdriver at the same time as I continue tapping. That works for me a surprising number of times. I have also found that it just wasn't going to turn sometimes, so I oiled it again, and repeated the same process the following day. It worked the second time for me on that particular screw.
   But allen wrench set screws are the pits! I can't help you there.

I was just going to ask that question too.

I also believe that the engineer's screwdriver is "hollow ground" at the tip. That is, the sides of the tip are slightly concave so that the very end of the blade has parallel sides. They also usually seem to be made of a much better quality metal, harder that is, at least the few I have seen. The tip of the blade stays in a screw's slot much better than the cheaper screwdriver tips, which are wedge shaped. I'm no expert, and I'm certainly not an engineer, but that is what I look for when I examine the tips of screwdrivers. They also usually have square shanks, which is very helpful. But lots of other screwdrivers have square shanks so that's not a foolproof identifier.