An advice and manners column I once read suggested you start (as in, you have no real history with this person, and you've had little communication before this point) written communications off formally—the Professor title is superior to, and trumps, the doctor title, for the record— and then from there address them in accordance to how they sign their responses. If you write to "Professor Jerrys" and he signs his response "Ben", then he has given you implicit permission to address him as Ben, and it would be appropriate for you to do so in the future. The nature of how they write their message will also give you indicators: if they're saying "howdy" to you then they're not looking to be on formal terms with you, and things like that.
When in doubt: ask them directly. Everyone's familiar with this problem and has gone through it themselves.
In my experience, in the US once you have your doctorate you can be on a first-name basis with your university's faculty by default: at that point you are officially their colleague. For some professors this extends down to their doctoral students, others to all graduate students, and to yet others it applies to everyone. The state you're in can even affect the level of formality a typical faculty member expects from any given person, due to slight cultural differences between states.
Note that this will change wildly from culture to culture. In France, for example, it's a flat hierarchy with essentially no titular addresses. Students invariably address their (male) professors as "Monsieur", and a famous professor could be teaching problem sessions to a lecture run by an unproven fresh hire. Which is not to say there's no social hierarchy at all (the famous guy will most certainly be treated more nicely than the new guy and given more deference), it's just that an institutionalized hierarchy is nearly non-existent. Japan, on the other hand, is very formal (in some ways the language is really two languages: one formal, the other informal) and a first-name basis is generally reserved only for very close acquaintances, like family members and lovers (even friends may still address each other in a formal way).
On that note, I just remembered a story a colleague once told me about the time he spent in Britain. There, he said, the extremely important and powerful guys that had a dozen titles (doctorate, professor, head of multiple societies, etc., for example) were always addressed as "Mr.". So if you were at a university, you'd know that those called "Dr." and "Professor" were pretty normal and weren't going to be the top dogs, but as soon as you were introduced to a "Mr." you knew you were in the presence of a very powerful and amazing man that you needed to show great respect to.