According to snopes.com (the urban legend source):
The "gas out" schemes that propose to alter the demand side of the equation by shunning one or two specific brands of gasoline for a while won't work, because they're based on the misconception that an oil company's only outlet for gasoline is its own branded service stations. That isn't the case. If one oil company's product isn't being bought up in one particular market, it will simply sell its output to (or through) other outlets. So motorists would end up paying more for it, because they'd be buying it at fewer stations. Oil companies do buy and sell from one another.
Prices at all the non-boycotted outlets would rise due to the temporarily limited supply and increased demand, making the original prices look cheap by comparison. The shunned outlets could then make a killing by offering gasoline at its "normal" (i.e., pre-boycott) price or by selling off their output to the non-boycotted companies, who will need the extra supply to meet demand.