Though the United States first started taking a national census in 1790, New Mexico did not appear until the 1850 census (7th). The New Mexico State Library has microfilm of the dicennial Federal Census of New Mexico for the years: 1850, 1860, 1870, 1880, New Mexico Territory Census of 1885, (the majority of the 1890 census was destroyed by a fire), 1900, 1910, 1920, 1930, & 1940. Note that there is a 72-year privacy restriction on census data.
The questions asked by census takers vary from year to year and from state to state. Detailed information about the questionnaires from 1790-2000 can be found in the Census Bureau publication Measuring America: The Decennial Censuses From 1790 to 2000 (available online).
Digitized census records are available on Ancestry.com (available in-building only, and through FamilySearch.org with a free account)
Indian Census Rolls, 1885-1940 (Record Group 75) Compiled by the Bureau of Indian Affairs, and arranged by Indian agency jurisdiction and year. Informational categories vary, but may include degree of Indian Blood, marital status and place of residences, along with name, age, and relation to the head of household. There are no indexes. This collection is available on microfilm and through Ancestry.com (in-building use only).