Way back in the Stone Age (late 80s), professors regularly hosted students at my school. The professor who was affiliated with our house would have the house officers over to his house a couple of times a semester. Other professors would frequently host the declared majors in their areas (as noted above, esp. the sciences), and then there was the Theatre Dept., where a couple of professors hosted notorious parties.
In grad school, there were a few professors who would host - the advisor to the Law Review would host them, the advisor to Moot Court would host them, etc., and certain professors would host top students in their subjects.
Then we had a couple of professors who were more infamous for their close relationships with their students.
