If you apply too much pressure to your Phillips screws, either from over drilling or just removing the screws too often, you can strip the heads. This removes the groves where the drill bit or screwdriver is inserted, making it extremely difficult to remove the screw. Here are a few different ways you can remove a stripped Phillips head screw.
Insert the Phillips screwdriver into the screw with the stripped head. Apply ample pressure to the screwdriver and rotate counterclockwise. As long as you apply enough pressure to the screw, there is a chance it will catch onto the screwdriver and rotate up.
Use a power drill to lift the head of the stripped screw above the surface of the object. Use a set of pliers to grasp the head of the screw. Hold onto the pliers tightly and rotate clockwise. This will be a slow process, but it will be effective.
If the head of screw is deeply embedded, drill through its centre about an eighth of an inch. Start with a drill bit a third the size of the head, and use larger bits until the head comes off. Grab the body of the screw with pliers and slowly and carefully twist it out.
Attach a square-drive bit to the power drill and force it inside the stripped Phillips screw head. Sometimes the square edges provide just enough grip to lift out the screw.