Since we're on a kick of adding privacy features, how about something for groups as well?
Simple addition. Group owners/officers may opt, already, to hide the group in peoples list as well as from search.
But suppose that you, personally, don't want to advertise your membership in a particular group? What I'd like is an additional checkbox for members that allows them to opt out of listing a group in their profile. This assumes that the group is set to list by the officers. If not, then the box would gray out and become a non-issue.