Yeah, stripping screw heads by digging at them in futility with a screwdriver is not the way to go. Instead, insert the screwdriver tip into the screw head then beat the crap out of the screwdriver with a hammer while putting =slight= counter-clockwise pressure on the screw. Works most of the time (unless you've already ruined the screw head) and is a great way to work off a little pent-up aggression!
n.b., dribbling a couple drops of Liquid Wrench or similar down over the screw before the Beating Treatment and letting it sit until it drains down inside will help.