When I was in law school, all our professors gave us their e-mail addresses, office numbers, and HOME numbers to encourage us to communicate with them outside of class. Most were gracious about being approached during office hours and were great about e-mailing people back.
I am currently in grad school in an online program, where I live two hours from the city where the university is based. One of my two classes has one live meeting a month (all day on specific Saturdays) and the other is based completely online. As a result, e-mail communication is absolutely necessary, but we also have class discussion boards and even an anonymous “Vents” forum – kind of like my own class’ version of The Pit. The impersonal nature can be quite frustrating and is a major culture shock for most students (and even the professors are pretty new to it), so we’re all trying our best to make it work under the circumstances. E-mail and message boards are NOT the best media to communicate subtleties such as emotion or tone of voice, so occasionally people get curt or harsh, and others take offense to relatively innocuous things. But communicating with my professors is a necessity, and visiting them during their office hours is an impossibility.