Official site of the U.S. Census Bureau. Includes the Decennial Census, 2000-2010, and the American Community Survey (ACS), an on-going survey. Both have demographic data at the national, state, county, and place levels, but ACS does not include small cities and towns. Data is in tables which can be downloaded.
The demographic data available includes age, income, gender, race, educational attainment, and more.