Is it appropriate to reply every time to a professor's "thank you" email? I want to know, since I am not a native English speaker, whether or not it is appropriate to reply to a thank-you email from a professor? 

For example, if every time you get an email from a professor saying "Thanks," you reply "no problem" or "you are welcome."

Could it turn out to be annoying or offending if one replies to every "thank you"?

I realized sometimes misunderstanding may unnecessarily arise because of cultural differences. If one does not reply to a thank-you email from a professor, then would the professor be accordingly offended? On the other hand, if one constantly reply "you are welcome" or something like this, would he be instead considered prudish?
Email exchanges need to end at some point.
If the professor's email is a simple receipt of correspondence, then I don't think there's a need to reply. However, if the professor has initiated a larger email then a reply is probably appropriate. See these examples:

Thanks sent as a form of receipt:


  Student: Hi Professor Smith,
  I've run the analyses you have suggested (see attached),
  Cheers,
  Mike


Then the professor replies:


  Pofessor Smith: Thanks for that


In this case, I think there is no need for the student to reply "You're welcome".

It wouldn't be a big problem, but it would be mildly distracting for the professor. Email exchanges need to end. The professor's "thank you email" was already a confirmation email indicating receipt of your original message.

Thanks sent by professor as part of a larger email initiated by the professor

Imagine the professor sends you an email that provides detailed information that also includes a thank you.


  Professor Smith: Hi Mike, well done on your work in the lab the other day. You did a really good job of fixing that equipment. I really appreciate it.
  Cheers,
  Professor Smith


In that case it might be appropriate for the student to reply: "you're welcome".