Attempts to remove a tight screw can often ruin the slot. If the head is above the surface, use a hacksaw to cut a new groove at a right angle to the original slot. Exert pressure evenly, not jerkily, with a screwdriver to ease out the screw.
Or remove the screw by gripping the head with locking-grip pliers.
Where a slot is ruined and you can't get a grip on the screw head, guess the size of screw shank and select a twist drill of the same size. Insert this into a power drill and use it to drill the head of the screw. Eventually the head will drop away. Remove any fitting, then turn out the screw shank with a mole grip. But be warned; there are some modern case-hardened screws which cannot be drilled out in this way.
If a screw has rusted in place, try applying the tip of a hot soldering iron to the head. The heat will expand the screw head and may loosen the rust. Or try easing oil around the screw.
