Stripped threading is a problem no matter where you encounter it, but it can be particularly frustrating when it shows up on your gas cap. This has become more of a problem in recent years with the advent of the locking gas cap. Fortunately it's not terribly difficult to remove these caps, though there is a trick to it.
Attempt to remove the gas cap by pulling on it while twisting in the direction normally used to remove it before trying to use any type of tool. A stripped thread can be skipped by applying outward force in this manner, and gas caps often provide plenty of room to do this with only your fingertips. Alternately, pushing in on the cap while turning -- in much the same manner as you would with a childproof medicine bottle -- may have the same effect.
Use a flat piece of plastic or soft wood as a makeshift pry bar to apply force to the back side of the gas cap while you twist it. Never use metal, as it can and will scratch your paint when the tool inevitably slips.
Purchase a tool designed to remove stripped gas caps. These typically run in the $15 to $30 range, depending on the quality of the tool. Alternately, you can take your vehicle to a local repair shop and have the cap removed for about the same price.
