The Census is the most comprehensive demographic survey in the United States. Although the questions asked change from year to year, there are always variables related to age, race and ethnicity, languages spoken, education, ancestry, income, home ownership versus renting, and more.
Google's new Dataset Search provides one-stop access to data, primarily in the social sciences, stored in thousands of repositories across the web.
The search is in beta as of September 2018, so please feel free to let me know if you find this a useful resource.