As a University of Massachusetts (public) faculty member, I have been told by several US hotels that I'm eligible for a government rate, even when my travel isn't related to university business. Doesn't work outside the US, unfortunately.
The savings tend to be largest at medium-high but not top-end hotels. The extra-fancy ones don't have to cater to government travelers. Cheap places don't have to cut their rates as much to fit under the per diem limits. (Motel 6 doesn't have a government rate at all.)
I've often found the government rates to be better than rates negotiated by the biggest employer in the vicinity, such as at the Marriott right next to NCR in Dayton.