WhoaNonstop wrote:To be completely safe I wouldn't.
I would always go by Dr. Last Name unless they specifically said not to. (As for when I'm a professor, I will insist on my first name only)
This is correct. I get plenty of suck e-mails, and either Dr. or Prof. is best. Sometimes Mr./Ms. is ok, and that isn't unusual for foreign students. First name seems awkward, even though I tell all of our current graduate students to call me by my first name (but I don't insist---most Asian cultures tend to resist first names for professors).
But then why do professors often respond with the first name? Well, suppose I were to get an e-mail from someone named Riley? I can't use Dr. or Prof., so the only option is Mr./Ms. But which is Riley? If I guess wrong, it is very embarrassing. So I will often respond with the first name, which is safer.