I'm not a believer, haven't been since I was twelve.
Alcoholics Anonymous and the people there saved my life. Flat out.
I decided right away, about three pages into the Step Book, that it was more important for me to stay away from a drink than carry on an imaginary battle with the "God thing."
Lots of atheists in AA, including my sponsor and half the friends I made.
(Disclaimer: I have to admit this was all long before there were all the alternatives people have been listing in this discussion, but, still, I believe I would have stuck with AA and the people there....not only that, but I know that if, God forbid!!, I were to start drinking again, I would go straight back to AA.)