The New York County, Division of Old Records at 31 Chambers Street, 7th Floor has them - or at least some of them - on film. I looked at some of them there a few years ago. However, it is not the best place for viewing the films. You have to take the films down to the first floor library really for viewing and printing copies. So, if you are local to the city, I think that Lynn's suggestion to go to the NYPL would be better.
The FHL in Salt Lake has the NY State census for NY County for 1855, 1905, 1915, and 1925 on film. They also have the 1890 Police census for Manhattan/parts of the Bronx. You can rent the films and view them at your local family history center.
As others have stated, they are not name indexed and you need an address or neighborhood/area to really start looking. If you have an address (or several addresses to explore), you can use the Stevemorse site (those wonderful folks!) to determine which AD/ED your target address would be in. It will also give you the FHL film number.
Here is the link to the NY State AD/ED finder at Stevemorsehttp://stevemorse.org/nyc/nyc.php
For the 1855 NY State census for NY County, you should find a map with the Ward boundaries. I probably have one somewhere - just not sure where at the moment. You can also use this Ward boundary description. It should help.http://www.bklyn-genealogy-info.com/Ward/1855.St.ward.html