Nothing is worse than preparing to perform some simple or needed repair only to find it impossible to remove a necessary screw. When a screw is overtightened, forced into wood or metal with a power driver too quickly, or simply not used properly, the head may become damaged and a screwdriver cannot make enough contact with the head to remove it. Several possible solutions and some special tools can help, but it may still take some time, perseverance and luck to get it out.
Stop struggling to get the screw out the moment you discover that the head is too worn to come out easily. Don't make the situation worse by digging and destroying what's left when you know it isn't working.
Put away the power drill and use a manual screwdriver instead. Drills will sometimes jerk into motion and tear at the screw head. Manually it's possible to turn the head slowly, evenly and with enough downward force to dislodge it.
Purchase a special screw extractor tool designed for use with difficult-to-remove screws. It is basically a screwdriver with strong metal threads that bite into the screw and keep it from slipping. It requires a lot of downward force while turning very slowly, but these helpful tools often work.
Try a different-sized screwdriver to see if that works. Some small-head Phillips screws will get worn, but then become wide enough to accept a bigger head driver. Sometimes square, star-shaped, or hexagonal drives will grab the rounded-out area.
Tap a screwdriver lightly into the screw head with a hammer before turning it. It requires finesse and doesn't really work with all screws. Soft metal screws are sometimes dislodged this way, but the amount of force used should be watched to avoid further damage or risk removing the head entirely.
Drill into the screw to destroy it. This last-resort option only really works well when removing screws from metal. It works by using a drill bit the same size as the original screw. Do this only if there is no other option.
Using a flat edge of a rubber band between the screw head and driver will give added grip if used with enough pressure and slow rotation. If the head is raised slightly, it may be possible to grab the top with locking pliers and turn it enough to get it started. Heating the screw may also help loosen it enough that it will be possible to get the screw to rotate out again.
When working with a screw, use eye protection if you are using power tools to try to remove it. Broken heads can shatter and spray out.