Professor

Professor was a title given and used by a variety of people throughout history, usually (though not limited to) peoples with university-awarded titles.

Ace referred to the Doctor as Professor throughout her early association with him (DW: Dragonfire et al) and still continued to refer to him as 'Professor' in a friendly manner several years later. (NA: Happy Endings) Allthough sometimes this irritated the Doctor, he grew used to it

In the year 100,000,000,000,000, Yana was given the title of professor, despite there having been no universities for over a century. (DW: Utopia)

Specific professorships
Bernice Summerfield originally faked her qualifications as a professor of archaeology; however she did eventually obtain a professorship. (NA: Love and War, Return of the Living Dad)

River Song introduced herself as a professor of archaeology. (DW: Silence in the Library)