The US government polls US residents once every ten years to create a statistical profile of the country according to a wide range of characteristics. There are many ways to access this information to research current and historical populations, including the ones listed below.
American Fact Finder is the US government's portal to census data. It's connected to census.gov because they work with a lot of the same information, but you'll find different views of the data on each site.
Social Explorer is an independent company that helps people create visual representations of census data on maps. The New York Times uses Social Explorer to create their interactive population maps, like the Immigration Explorer they created a few years ago.
The Historical Statistics of the United States covers population, work and welfare, economic structure and performance, governance, and international relations, from colonial times to the present. It includes census data, but it's more than that. You may find that the essays included are helpful because they can help place the statistics in context.
The New York Department of Health tracks Vital Statistics for the state. You can also request copies of birth, death, marriage, and divorse certificates through the agency.
The New York State Archives and Ancestry.com have teamed up to digitize family history records and make them available on line for free.