The Oregon Historical Society Library, Oregon State Library, and Oregon State Archives each have federal census records for Oregon available on microfilm. The Oregon Historical Society Library is also home to supplemental schedules.
Censuses were regularly taken of the territory and then the state. Those census records were taken in the following years: 1842, 1843, 1845, 1849, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 1865, 1875, 1885, 1895, 1905
In several cases, only some of the records have survived from a given census. Generally, only the names of heads of households were recorded, but the census records for 1895 and 1905 do include information about other people living in each residence.
The Oregon State Archives website “Oregon Historical Records Index” database includes an inventory of state census records. Also, most of the state census records for Oregon are on microfilm at the FHL.