The head of the screw you stripped while you were hanging that shelf may not have seemed like a big deal at the time—until you needed to unscrew it, that is. Next time you're having trouble, try a rubber band.
Home hacks and design blog Apartment Therapy offers a a few simple, smart tips for removing a stripped screw without any special equipment like an extractor—like using a rubber band:
A rubber band may aid in providing enough grip to remove, or at least loosen, the screw. Place a wide band rubber band [in between] the screw driver (we recommend bumping one size up from the screw head which caused the strip) and the screw, then apply hard, but slow force as you turn. If you're fortunate, the rubber band will fill in the gaps caused by the strip and allow extraction.
They also suggest more obvious solutions like changing the size of your screwdriver, using pliers when possible, or just pounding the screwdriver into the screw head with a hammer, hoping you can create your own traction. If you've ever tried the rubber band trick—or have your own favorite method—let's hear how it worked in the comments. If your screw's just fine but your screw hole is stripped, a golf tee may be all you need.
How To Remove a Stripped Screw Without an Extractor [Apartment Therapy]