When meeting a professor for the first time, is it always a good idea to ask about their research interests?
Two points from experience (as a student):


Don't ask/talk about something that can be googled


If you want to talk about the professor's research interest, that's great but the key point is not to talk/ask things that can be answered in a Google search. Asking a professor about his research interest might qualify as one of these cases. Checking his webpage (if updated) might answer the question. "Why did you use X instead of Y in your paper titled Z" might probably be a good question to ask (depending upon the occasion). 
Now that I reread my answer, I feel professors are like SE sites. Ask closed non-google-able questions while showing interest and initiative and you will have a good time.


Gauge the occasion


Needless to say, meeting a professor for the first time in an orientation party, conference or a course orientation might call for different "first conversations". Don't force what you want to talk about on the professor. (But then, this is true for all people not just professors.)