A wide variety of options exist online for searching and viewing digitized copies of U.S. census records from 1790 to 1940. Several subscription-based sites offer the entire run, with seamless searching and browsing. However, if you only need access to a few census records, or are particularly budget-conscious, you can also achieve free access to the entire U.S. census run 1790-1940 with a little extra effort.
Heritage Quest Online offers free access to all U.S. census images 1790-1940 (and select indexes) to anyone who has free access through a participating local, state, or university library system. Contact or check the website of your local public library, as well as your state and any nearby university libraries, to see if they offer remote access to Heritage Quest Online and if you are eligible to apply for a library card. Alternatively, you can use the free census indexes available on FamilySearch, in combination with the free digitized U.S. census images on Internet Archive (no indexes) to achieve free access to the entire U.S. census collection 1790-1930. The 1940 U.S. census (not necessarily other records) is completely free from several sources, including Archives.com (not to be confused with Internet Archive--archive.org), Ancestry.com (free account required to view records), FamilySearch.org, MyHeritage.com, and FindMyPast.com (free registration required).
Learn more in Sources for U.S. Census Records Online