If it comes to the worst, there are still things you can do.
1) If the stripped fastener is accessible (i.e., not down a hole) you can try cutting a new cross slot in a screw head or new flats on a nut using a Dremel tool with a cutoff wheel (or a small file, if you're old-school). This is also an option for any special fasteners that you can't get a driver for.
2) You can (carefully) drill the screw head off, then, once the piece immediately below the screw head is loose and has been removed, grab the stub with a pair of vise grips and turn it out.
3) If it's in plastic, you can heat the screw head with a soldering iron until the plastic surrounding the screw body melts and the whole thing can be pulled off (obviously this is going to result in damaging the plastic to some degree... you may need to use a larger self-tapping screw to put it back together, or you could put a small amount of hot-melt glue down the now-oversized hole, in case you need to do it again).
As others have said, hand drivers are a better choice for this than powered drivers. If you do use a power driver and it has adjustable torque, start at the lowest setting. And yeah, as much downward pressure as you can apply without breaking the case is a good idea.
1) If the stripped fastener is accessible (i.e., not down a hole) you can try cutting a new cross slot in a screw head or new flats on a nut using a Dremel tool with a cutoff wheel (or a small file, if you're old-school). This is also an option for any special fasteners that you can't get a driver for.
2) You can (carefully) drill the screw head off, then, once the piece immediately below the screw head is loose and has been removed, grab the stub with a pair of vise grips and turn it out.
3) If it's in plastic, you can heat the screw head with a soldering iron until the plastic surrounding the screw body melts and the whole thing can be pulled off (obviously this is going to result in damaging the plastic to some degree... you may need to use a larger self-tapping screw to put it back together, or you could put a small amount of hot-melt glue down the now-oversized hole, in case you need to do it again).
As others have said, hand drivers are a better choice for this than powered drivers. If you do use a power driver and it has adjustable torque, start at the lowest setting. And yeah, as much downward pressure as you can apply without breaking the case is a good idea.