[Turing_Machine]

The social rule I was taught (in the U.S.) is that if you have a PhD in whangabangology, it's okay to call yourself "Dr. Blah" or "Joe Blah, PhD" in a professional context (writing a paper on whangabangology, or teaching it, or giving a professional talk, or appearing at an official university function), but not in a social context (making a restaurant reservation, say, or being introduced to someone at a party).

Professional usage varies a lot by institution. Where I went to grad school, undergraduates usually use "Doctor" or "Professor" when addressing a member of the faculty, but graduate students usually call the professors that they actually know by their given names. I understand that's not the case everywhere; at some schools even grad students who have worked with a professor for years are still expected to address them by title. I have heard (but have not personal knowledge one way or the other) that the University of Chicago is one of these.