Under what circumstances would a professor be offended at students taping or recording his or her lecture? Are there any policies on taping or recording or even streaming a professor's lecture? 

What do professors think about students who do this? 

Obviously, most circumstances the professor would never find out, but there was this one instance when a professor got really angry because a student was recording him without his permission. 

I don't understand why he would be offended, most likely the student is only using it for review and not commercial purposes as the nature of the class is quite obscure, could anyone shed a light?
I do not believe it had anything to do with the act of being recorded by itself. Most universities are beginning a process of recording lectures for later consumption by the students anyway.

Instead in this case it is likely because the professor was unaware they were being recorded. They may do or say something that they regret or which gets them into trouble. If however they knew beforehand that they were being recorded it would be unlikely that they would do that since they know the repercussions would be more severe. I think it was an instinctive reaction to protect themselves from others using the recording against them.