Digital-Topo-Maps.com, Quickfacts.Census.gov and MapsofWorld.com offer free county maps of all states, as of 2015. All three websites allow you to display a colored map of county boundaries by selecting a state.
Find a map of a state's counties on Digital-Topo-Maps.com by clicking the state of choice near the bottom of the home page and clicking the colored map of that state on the bottom of the next page.
To find a map of a state's counties on Quickfacts.Census.gov, click the state of choice on the U.S. map, and then click Selection Maps on the left side of the next page.
On MapsofWorld.com, display a county map of a state by clicking the United States on the world map, clicking the state on the U.S. map and clicking Counties on the next page.