The U.S. Census Bureau publishes its findings on Census.gov, although I often find it easier to get Census Bureau data for a particular location using using State & County Quick Facts.
You can design your own table of census bureau data using The American Factfinder. Links to other search tools are posted at www.census.gov/main/www/access.html.
For more information, call the Census Bureau (202-264-0634) or read the extensive information on the Bureau's web site.
American Community Survey: As of 2010, the Decennial Census has been limited to a short form designed primarily to count the population. The more detailed information once collected on the "long form" is now gathered on a continuous basis in the American Community Survey. The Survey began in 1996 and is also administered by the Census Bureau.
Historical Census Data: The Census Bureau is allowed to release data from individual families after 72 years. Census records from the 1930s and Census records from the 1940 are posted by National Archives and Records Administration. Ancestry.com and the Minnesota Population Center are working on a project to make the 1940 census searchable by name (free with registration).
For older information, the Census Bureau posts selected historical census data back to 1790. Historical data (pre-2011) can also be found in old editions of The Statistical Abstract of the United States, the State and Metropolitan Area Data Book and the County and City Data Book; check Worldcat to find libraries holding back editions. Ancestry.com has a U.S. Federal Census Collection going back to 1790, including a recreation of the 1890 Census that was destroyed in a fire (subscription).
Foreign Census Data: Links to the Web sites of foreign census agencies are posted at www.census.gov/main/www/stat_int.html. Ancestry.com has UK Census Collection. and a Canadian Census Collection (subscription).