Alcoholics Anonymous (or AA) is the "granddaddy" of all twelve-steps groups. In fact, they developed the whole twelve-step model. (If you're not familiar with it, it's the process of going through the steps involved in recovery in an organized, bite-sized way. You do it one small "step" at a time, until you've completed twelve of them). Following on the heels of AA came groups such as Narcotics Anonymous (NA), Cocaine Anonymous (CA) and many others. All of them follow the same basic structure, and just tweak the wording of the Steps enough to apply more specifically to their members' addictions or compulsive behaviors.
More recently, Saddleback Church, pastored by Rick Warren, developed a distinctly Christian alternative to AA and NA. It's called Celebrate Recovery. It also bears many similarities to AA and NA, but has some definite differences:
Not everyone sees the CR approach as contradictory to AA and NA. In fact, as a Christian myself, I support CR, but believe AA and NA can complement a Celebrate Recovery meeting. Personally, I feel more comfortable specifically identifying Jesus Christ as the only true "Higher Power." On the other hand, I'm unsure about whether every person is always an addict. I do, however, recognize the scientific evidence that says that addiction is a biological condition (I prefer calling it a "disorder," however, rather than a "disease").
Interested in checking out CR? They have a website at www.celebraterecovery.com. On that site, you can navigate to their "Groups" finder to locate a CR meeting near you.