I have used google+ hangouts to virtually visit another math teacher's class. Actually, there were 3 or 4 teachers visiting this particular class at the same time - in a google+ hangout. The teacher had sent us copies of his students' work on some old AP Statistics free response questions. He then would put work that was done by one of the students on the screen for everyone to see, including the teachers in the hangout. The teachers in the hangout would take turns questioning the student about his work and making comments that were beneficial to the entire class. It was pretty cool to visit a teacher's classroom that was over 200 miles from my own without having to drive anywhere.
What about Hangouts on Air? I have thought of one way this could be used in AP Stats. Before the AP exam, it would be nice to have a short "talk" with my students. With a hangout on air, I could do this not only with my students, but any other students who are interested in getting some last minute advice. I could even have my twitter feed active for students to submit questions. What might be even better is to get my AP Stat teacher friends to be in the hangout and we could all answer the questions in a tag-team sort of way.
So, no math here. But a few thoughts on how to use google+ hangouts.