Your question is a broad one. More clarification might be helpful.
Demography is simply "the statistical study of human populations especially with reference to size and density, distribution, and vital statistics" (Merriam-Webster Online).
Demographics are used for everything from pharmaceutical drug research to business marketing to employment practices. Scientific research often involves demographics of some kind, so there have been countless studies "in demography."
If you're asking how many studies have there been ABOUT demography, also called "population research," there are numerous universities that have demographic research programs in the field of social science, so those studies are countless as well.
Some university programs:
Western Washington University: http://www.ac.wwu.edu/~drl/
Penn State: http://athens.pop.psu.edu/allen/LinksByCat.cfm?SubjectID=6
Princeton: http://opr.princeton.edu/