The most recent (2000 onwards) data put out by the Census Bureau is obtainable via the data.census.gov.
On the Census Bureau’s main data page, there is the option for Quick Facts and Data Profiles, which are the easiest way to get information on population areas. Quick Facts is limited to areas with a population of 5,000 or more, while Data Profiles will give information on smaller areas, along with giving more information options.
If what you are looking for goes beyond the Quick Facts and Data Profiles options, the interface at data.census.gov gives two options. On the top page, users are given a search box to try a search. If searching through that proves fruitless, the “Advanced Search” option allows for a search to be constructed by topic, geography, year of survey, specific survey, and code (which is used for economic surveys.)
Historical Census Data is available. Users are limited by what questions were asked and what the Census Bureau decided to publish. This could mean that a town or county one is researching was too small for the level of detail in data that one finds with larger population areas. These volumes are available online, and the library also has an extensive collection of the publications in print.
The most up to date statistic put out by the Census Bureau is the estimated population of the United States, which is shown on their population clock page for both the United States and the world.
The Decennial Census is taken every 10 years, and it is the longest program of the Bureau, going back to 1790. As the decades have passed, the questions have changed to reflect the social and political currents of the era. Starting with the 1940 Census, a sample was taken with supplemental question, becoming the "Long Form Census" in 1980. After Census 2000, the Long Form ceased and was replaced with the American Community Survey.
The American Community Survey began in 2003, and is a survey of about 3.5 million households each year on social, economic, and housing characteristics. In order to both ensure respondent privacy and provide a good data pool, the results are released in different aggregations based on population size. There are annual estimates for areas with population over 65,000 people, 3 year estimates for areas with populations over 25,000 people, while the 5 year estimates are for all area, including zip code areas, census tracts, and block groups. The release of the 3 year estimates ended after the release of the 2011-2013 estimates.