The most recent data from the U.S. Census Bureau (2012) counted 35,879 general purpose local governments, which includes 19,519 municipal governments, 16,360 town and township governments, and 3,031 county governments.
For state-by-state details, see General-Purpose Local Governments by State: Census Years 1942 to 2012, 2012 Census of Governments.
For further information about special purpose local governments, including special districts and independent school districts, see Government Division Briefs, Government Organization Summary Report, 2012, Bureau of the Census. http://www2.census.gov/govs/cog/g12_org.pdf