Repairing a stripped screw hole should be one of the first things one tucks into a homeowner’s survival repertoire. There are many tricks in circulation that just don’t work, and so sticking to a tried and proven repair method will save you much time and frustration, not to mention that it should be done once, and done right.
The first thing might be the easiest. Try using a wider circumference and longer screw. It may be that there is enough of the wood left for the larger screw to do the job since it can still "bite" into the wood.
If replacing the screw hole that had been stripped requires something more, there are a couple of tricks to try. If your stripped screw is coming out of a soft wood like pine, an oft used easy fix is available. Take small wooden matches, place enough in a trio or foursome to fit the hole, and fill the remainder of the hole with wood glue, or even Elmer’s white glue. When your hole is packed pretty tight, and the glue has been allowed to dry, you may try replacing the old stripped screw with a new unstripped screw. If fixing a hardwood installation, using a few hardwood toothpicks works equally well.
Oftentimes there will be those who use an epoxy or other hard chemical fix, to drive the stripped screw into, but these "fixes" aren’t pliable or flexible enough for this type of repair, and so as the wood expands and contracts, the plug may drop out, or ruin the wood around it.
If your hole is found in drywall, then it may be time for a trip to the hardware store. There are available, simple kits for fixing stripped screws that are exceptionally easy. These kits contain a small plastic element to place in your hole, and when properly set, the plastic piece will hold the screw tighter than any repair might.
One last note, wood fillers that can be bought at the hardware stores are meant to cover up the top of the screw and help it blend into the wood around it with stain. It is not meant for repairs, since it may not hold up long term as a repair requires.