Federal censuses in the United States were taken in years ending in a “0” beginning in 1790. A variety of states have taken states 
in non-federal census years. Most of these records have been microfilmed (perhaps online at FamilySearch for free or Ancestry.com for subscribers) or are available at state archives or libraries.
Not all United States states took a state census.
3 Responses
Taken from Ann S. Lainhart’s book, “State Census Records” published in 1992. “State by state, year by year, often county by county & district by district, she shows the researcher what is available in state census records, where it is available, & what one might expect to find in the way of data” Because of the internet and FamiySearch continuing to add old records to their collections, more of these state census have been made available since 1992. I purchased this book when it was first published and still use it. What I like most about it is the description of what information each census should contain.
It is also important to realize there are many substitute Schedules or Census Type Listings
to use in place of the Census. All is available for Researchers at your State Archives or NARA archives that you or any researcher can obtain by contacting these Archives. Many are available on Microfilms via Interlibrary loan (also check LDS Catalog). Most of the Records (stated below) are not in Alphabetical order, however most are listed by State or Territory. Yes, it does take time and effort (also various fee charge) on the person requesting them to obtain them, but a serious researcher will find them invaluable with the information one can obtain. They will give you additional information (and most time more accurate) than any information obtained on the State or Federal Census. It can be the answer to the maiden name of the wife, the new surname if she remarried and all survivors.
We have the 1890 Veterans Census for Veterans or Pensioners for Union Service (also included some Confederate but they have other listings also) and their Widows (naming the name of veteran she collects Pension under). Also possible listing of children. Listing taken from the Pension Office from Bundle 198. Their Length of Service, Rank, Branch (Soldier, Navy), Living Address, DO Enlistment, DO Discharge, Disability. These record also include many from the War of 1812, Mexican War. If deceased during service it will give information how and where it occurred.
Since there was 150 years between the Declaration of Independence and forming the of NARA there are many record that are not available. They were from Alabama to Kansas (but not all) and over 50% in Kentucky. Regardless of all the myths that surround Genealogical Records all was not lost in the Fire of 1921 and many survived.
In addition to the above many other Census Record Types (other than State or Fed.) survive and are available to all Researchers. Some may be transcribed (but I hesitate to use when an actual record or microfilmed copy exists ) on the Internet but beware of errors in them.
Other valuable Census type Records or Schedules that exist and are available to you are some Territorial Census done in 1890 along with some 1885 State Census. We have many located at the State Archives and/or NARA on Agricultural Census Schedule, Business schedules, Manufacturing schedules, Mortality schedules, Social schedules and Statics Schedule. These have various valuable Genealogical Information listed. Getting up to the year 1835 under the Business Schedule one will find it even broke down to heading such as Advertising, Banking, Motor Trucking, Public Warehousing and Radio Broadcasters and etc.. Sharing my experience through the years using these available sources I have resolved many family mysteries
Thanks, Patricia, for responding and mentioning all those other census records that people sometimes forget (or are not even aware of). For those who are unaware of these sources, there are many good avenues to consider in this response.