This is an understandable reaction, and the logic makes sense on a first-pass basis: You stop buying BP gas — which comes from BP oil — which makes BP feel the pain and be more responsible. Or something. Unfortunately, the economic reality is very far from that simple scenario. The effects of a BP gas station boycott would be ineffective and/or undesirable for a few reasons:
1) BP gas stations aren't owned by BP — they're owned by independent franchisees. This means that if you boycott these stores in general, you're only screwing some poor guy trying to make a buck.
2) Oil is what they call a "fungible commodity" — this means basically that if you don't buy it, someone else will. Further, since boycotting BP stations means they'll just sell their gas wholesale elsewhere, the result could actually be marginally higher prices due to reduced suppliers.
3) Finally, even if a boycott did affect BP somehow (which it won't), one wonders how you reconcile this with the fact that we're trying to force them to clean up their mess. Hitting them in the pocketbook right now, in the midst of a truly unprecedented (and perhaps futile) clean-up effort, seems a bit ill-advised.
That's not to say that BP should go off scot-free, per se. I honestly haven't even delved into the details of how negligent they were and what safety regulations/rules were broken. I do know, though, that there are thousands of off-shore oil rigs in the gulf alone. BP just has the misfortune of being the guys this time around to fuck up in the process of feeding our oil habit. Last time it was Exxon.
Rather than approaching this whole thing from a vengeful/punitive angle, we should focus on ways to discourage off-shore drilling and reduce oil/gas consumption in general. So if you really want to hit BP where it hurts, skip the drive to work and take a bus. Ride a bike. And maybe stop at a local BP gas station and buy a snack on the way in!