Statewide Census Records that exist for New Mexico are 1850, 1860, 1870, 1880, 1890 (fragment, see below), 1900, 1910, 1920, 1930 and 1940.
There are Industry and Agriculture Schedules 1870 and 1880; the Mortality Schedules for the years 1870 and 1880; and the Union Veterans Schedules for 1890.
The Special Collections Library and the New Mexico State Records Center and Archives all printed New Mexico federal census indexes, as well as population schedules on microfilm. They also contain federal census source information.
The 1910 census is currently being compiled into an index by the Albuquerque Genealogical Society. The Special Collections Library has the completed county record publications on file.
Native American census records from before 1880 are not accurate. Many of them are incomplete as well. Regular census records were taken between 1885 and 1940 for Native Americans, but they weren’t taken every single year.
The National Archives is the best place to find sources for those records, but it’s important to keep in mind that the records vary greatly from one tribe to another.
The New Mexico State Records Center and Archives has many Mexican and Spanish colonial census records on file. However, the original records are recorded in Spanish. The University of New Mexico Special Collections Library and the Family History Centers have copies of those records on file, as do several other organizations in New Mexico.
The 1885 state census, in reality, was issued by the federal government. It lists all people living in each household. That census is on file at the New Mexico State Records Center and Archives.
However, some of them are illegible and others have been lost. Other locations also have copies on file, including the FHL, National Archives and University of New Mexico Special Collections Library.
New Mexico Colonial and State Census
Spanish and Mexican Censuses of New Mexico, 1750 to 1830. Albuquerque: New Mexico Genealogical Society, 1981. Spanish and Mexican Colonial Censuses of New Mexico, 1790, 1823, 1845. Albuquerque: New Mexico Genealogical Society, 1979. (Contains corrections of the 1975 edition, as well as new material.)