Ancestry.com provides access to all federal census records from 1790-1940. The 1940 census is the most recent one available to the public as privacy laws dictate that individual records from the federal censuses are confidential for 72 years. Patrons unaffiliated with William and Mary may only access this database in the library, though W&M personnel may also access it off-campus using their W&M login and password. Many other local libraries also offer on-site access to Ancestry.
The library has many census records, include state records, available in print and on microfilm. Below are some Virginia records, but many other states are available for a limited number of states. To see if we have a state, search for "census" and the state you are interested in the Swem online catalog. Additionally, indexes to all census are available on microfilm, but printed indexes are only available from 1790-1870. The microfilm is in the government documents collection on the first floor, and the indexes are on the shelves facing the microfilm cabinets (call numbers beginning with HA).
Also on the shelves facing the microform cabinets are privately published census indexes that make the microfilm rolls slightly easier to navigate. You can look up family names, and they will direct you to the correct roll of microfilm. The rolls themselves are labeled only with year and state, so these indexes will save you a lot of time.
The library has some census schedules on microfilm for other states from 1790-1830 (North Carolina goes through 1850), but the corresponding printed indexes may not be there.
Swem Library does not have the Soundex microfilm collection, though this is available through Ancestry.com.
Here are a few other websites that might be of interest. They are not exactly "genealogical," but can give you a good idea of what America looked like over the years via the census and background on the US census: