Have people been prosecuted for using fake degrees?
See here for one case:

http://www.employeescreen.com/iqblog/fake-degree-leads-to-arrest/

And here's the official announcement:

http://www.nyc.gov/html/doi/downloads/pdf/pr46feraca05_26_2010.pdf

Apparently, in the US, one can be charged with "criminal possession of a forged instrument" and "offering a false instrument for filing".

However, this case concerns a fake degree from a real institution. As noted below, the Diploma Mill case is much more complex. See here for a discussion of the legal issues:

https://journals.law.stanford.edu/sites/default/files/stanford-law-policy-review/print/2010/01/gollin_21_stan._l._poly_rev._1.pdf