university - How to address a professor in letter?

When writing letter to an academic professor (not necessarily from student to professor), what is the appropriate way to address his/her title?

I have seen in letters using

Dear Prof. X even when the addressee is not a full professor

Dear Dr. X though, knowing that the addressee is a full professor

Dear Mr/Mrs X though, knowing that s/he has an academic title

Answer

The appropriate way to address someone is with their proper title. In your question, it seems you know what the title should/should not be. If you know, use it. If you don't know, it's generally safer to err on the side of formality.

While I personally prefer (and request) everyone to refer to me by my given name, I do feel it a little strange when someone I do not know / have never met addresses me in writing by my given name. Perhaps I am old fashioned but I expect introductions to be formal (and better to be too formal than too familiar) and then quickly get to preferred ways of addressing (i.e., to use my given name).

When corresponding (in writing or electronically) I would look to the signature. If they wrote:

Dear Professor Schmoe:

Blah blah blah


Sincerely, 
John

----- 
Dr. John Doe 
Agri-science Department 
University of Whatchamacallit

Then I would write back

Dear John:

Thank you for your letter. Blah blah blah.

Sincerely,
Joe