Those calling for a boycott (via the media and Facebook) seem to be convinced that filling up one's gas tank elsewhere will somehow teach BP a lesson, or at least impact its bottom line. The lion's share of BP's revenue comes from its production arm selling crude oil to the open market, not from its franchises selling Snickers bars and gasoline. Any petroleum-based product you buy today could have been manufactured with oil from BP's production company.
BP's revenues/profits are completely dependent upon the price of crude oil, which is driven for the most part by Western European and American consumption.
So if you want to boycott BP, cut back in general. If you want to boycott BP, take a walk rather than a drive. Because driving past a BP station and filling up at Exxon/Shell/Sunoco is not helping with the disaster in the Gulf whatsoever.