Types of census were also taken prior to the first federal census of 1790. In addition, some states took enumerations between the decennial years, either state or federally funded. An example of this is Iowa where state censuses were taken from 1836 through 1925. Images of many of these can be found online, particularly at Ancestry.com Some of the other state censuses can also be found at http://www.FamilySearch.com
Most researchers are unaware of the U.S. Special Census on Deaf Family Marriages and Hearing Relatives, 1888-1895. The Volta Bureau of Washington, DC, founded in 1887 by Alexander Graham Bell, promoted research with regard to the marriages of deaf people in America. Questionnaires were distributed to deaf couples and family members of deaf individuals. The questionnaires were completed from 1889 to 1894 with the following information:
Names of husband and wife
Whether deaf or hearing
Age at which deafness occurred; cause of deafness
If attended school
Details about couple's marriage (date and place)
Details relating to couple's children (number of children deaf or hearing, names, dates of birth or death, causes of death)
Details relating to husband's and wife's parents; brothers and sisters
There are multiple pages in each of the files for this census. Particularly for the time period and the questions asked, it is beneficial even if you do not suspect deafness in your family. Images of this can be found online at Ancestry.com.
An often overlooked enumeration is the US Federal Census - 1880 Schedules of Defective, Dependent, and Delinquent Classes. This pertains to collected data on the insane, idiots, deaf-mutes, blind, paupers and indigents, homeless children and prisoners. Information consists of name, race, gender, age, residence, and medical history pertaining to mental and physical illnesses. This enumeration is also available for some states on Ancestry.com or microfilm at the Family History Library (LDS).
Online images of any of these enumerations are indexed. However, always check one against another. Errors crop into the indexing process. I have also found missing pages from one Internet site to another. Even if you think your ancestor was normal, it's a good idea to check some of the special census records.