If a professor is teaching a student currently, is it okay if he/she friends the student on social media sites such as Facebook or Google Plus?
It depends a little on the circumstances, but generally not. If the student is your Ph.D. student, then it's probably OK to accept a friend request, but you shouldn't initiate it (and some people might not even approve of accepting it, depending on the sort of advising relationship you have). If it's an undergraduate in one of your classes, then I don't think you should even accept a friend request, and sending one would be very improper.
There are three basic principles:
You shouldn't put your students in situations where they might feel awkward or uncomfortable. For example, would turning down a friend request from one's professor come across as rude?
It's not healthy for class dynamics if there's a perception that you have a closer, friendlier relationship with some of the students than with others.
You need to be very careful not to do anything that could be misinterpreted (or, worse yet, correctly interpreted) as showing romantic interest. Some people will interpret things that way if it's even vaguely plausible, and fair or not you've got to keep this in mind.