Screw loose in screw hole. Remove from hole and cram hole with steel wool, solid wire solder, plastic wood, or a glued wood plug. Then reset screw.
Screw "frozen" in place. Heat screw head with a soldering iron. Then unscrew it.
Head damaged so that screwdriver wont hold. If necessary to salvage screw, reslot head with a hacksaw.
Shank broken off in wood. If wood is thick enough and new screw must be reset in same place, drive screw deep into wood with a nail set. If this is impossible, punch a small hole in the top of the screw with a steel punch. Then drill out screw with an electric drill.