In the 1990s there were two operational systems--GPS (US) and Glonass (Russia)..
Europe's Galileo was a program planned which involves launching new hardware; a good description of their short-term plans is "Europe provides Satellite Navigation Services", 28 Jun 1996, and a description focused somewhat more on long-term plans and overall strategy is "Europe's contribution to a navigation satellite system", 11 Jun 1995, both from the European Space Agency. Or for a more recent update see "EU to launch homegrown satellite navigation system", CNN Interactive, 17 Mar 1999.
China is planning a system with two geostationary satellites to be launched by 1999 and Japan is likely to approve an experimental regional system to be launched in 2002. The source is "China, Japan Consider Navigation Systems" from the online Space News for 14 Oct 1996, but the online version requires registration and as far as I know doesn't keep back issues. I haven't tried to find out whether this article appeared in the paper edition.
Use of these systems is expanding rapidly (see for example "Positioning and Navigation", Trends in Commercial Space - 1996, Keith Calhoun-Senghor, Editor, Office of Air and Space Commercialization, U.S. Department of Commerce), but that by itself doesn't translate into additional launches, because the satellites can serve an unlimited number of users. What determines the number of launches is the progress of the European, Japanese and Chinese systems, and whether Glonass stays alive given the continuing funding problems throughout Russia. Continued replacement of GPS satellites as they fail can be fairly well assumed, I think.