Quoted from here: http://en.wikipedia.org/wiki/BFG_9000
The abbreviation BFG stands for "Big F***ing Gun" as described in Tom Hall's original Doom design document. In the Doom II user manual, BFG is said to stand for "Big Fragging Gun". Another name, according to the motion picture, is "Bio Force Gun" (although in the movie itself, "Big F***ing Gun" is spoken as it comes into view). In the Quake II manual it says it stands for "Big, uh, freakin’ gun".
(Extra asterisks added by mysef.)