The Rochester (NY) Genealogical Society's (RGS): New York State Census
This is an excellent resource, including links to colonial census data from New York. Additional information from the RGS site:
"Existing original census records are usually in the County Courthouse or with the County Historian.
The LDS Family History Library has the most complete collection of films of the New York State census. It is said that the LDS does not have every existing census. Another place that has a large collection of the New York census records is the NY State Library. To see what is in their collection, go to their New York Census page. It is important to note that none of the microfilm at the NY State Library circulates while the LDS lends all filmed census."
The RGS Web site also has a online list of the questions asked in each New York state census and a county-by-county lists of the microfilm of the schedules available for loan from the LDS Family History Centers. As of this writing, film is available from the 1825 to the 1875 censuses.
Information for the Latter Day Saints Family History Center in Ithaca. (The following information is taken from the Family History section of the national LDS Web site).
Address: 114 Burleigh Drive, Ithaca, Tompkins County, New York, United States
Hours: Tuesdays, 11am-4pm; please phone to verify the center is open.
Notes: Closed the last two weeks in December and Thanksgiving week