Close friends, immediate family, and others in recovery. And only if it comes up. I have no reason to share it with anyone else, and learned a lot about who NOT to share it with in my first few years sober. I told people at work, and at school when I began college - and it came back to me in negative ways in both instances. I also learned a lot in the first 2 years about the principles behind anonymity, but they apply only to those in AA. I respect those principles and traditions because they're in place for the protection of AA. That part has little to do with me.
I find it's often more difficult, more character building, and even more honorable to remain anonymous - than to tell people I'm in recovery. For me. And it's got nothing to do with shame, as some people believe. It has more to do with pride, actually. It's easy to want to tell the world how great we're doing
.