The Census Bureau has a nifty, interactive map that lets you follow the center of the population through American history:
The center is determined as the place where an imaginary, flat, weightless and rigid map of the United States would balance perfectly if all residents were of identical weight. … Historically, the center of population has followed a trail that reflects the sweep of the nation's brush stroke across America's population canvas. The sweep reflects the settling of the frontier, waves of immigration and the migration west and south. Since 1790, the location has moved in a westerly, then a more southerly pattern. In 2000, the new center of population was more than 1,000 miles from the first center in 1790, which was near Chestertown, Md.
(Hat tip: Mother Jones' Tumblr)