Use a rubber band or thin steel wool between the tool and screw head for extra grip
Try a slightly larger or better-fitting driver bit to improve contact
Use penetrating oil (or a penetrating lubricant) and wait, then re-try removal
Apply heat to the surrounding material (carefully) to loosen corrosion, then try again
Cut new grooves in the screw head with a Dremel/rotary tool and remove with a flathead screwdriver
Use a screw extractor kit (spiral/spiral-flute extractor) sized for the screw
Drill a pilot hole for the extractor, then install the extractor and turn counterclockwise
If the screw head is stripped, drill out the head, then remove the remaining shank with pliers/locking pliers
For screws in wood, use a left-hand drill bit to back the screw out while drilling
For screws in metal, drill out the screw shank and remove the remainder
Use pliers or locking pliers on any exposed portion of the screw shank
Weld or braze a nut to the stripped screw head, then remove with a wrench
Use a thread-cutting or reverse-thread screw/bolt extractor designed for stripped fasteners
If all else fails, drill out the screw completely and replace with a new fastener