The US Census Bureau is the primary source of demographic data in the United States. The two most important resources are the Decennial Census of Population and Housing, a complete enumeration of the entire population conducted every decade since 1790, and the American Community Survey (ACS), an ongoing survey conducted since 2005. For a more detailed explanation of these surveys, please see the research guide for Population Data From the US Census.
Census and ACS data are available from a number of resources. The following is only a partial list.
Data.census.gov is a portal from the US Census Bureau that provides access to a number of their products, including the ACS and Decennial Census data from 2000.
Social Explorer (licensed resource) provides access to many census and ACS variables, including some data as far back as 1790. Social Explorer has the benefit of an intuitive map-based search tool with spatial querying capabilities that make it convenient for neighborhood scale analysis.
Infoshare is a database of survey results and statistics for New York City at a variety of geographies. ACS and Census data are available as far back as 1990. Data tables can be generated at a wide range of geographic levels, including NYC-specific geographies including community districts, police precincts and neighborhoods.
National Historical Geographic Information Systems (NHGIS) provides access to census data (and boundary files) at a variety of geographic levels as far back as 1790.
NYC Department of Planning provides a variety of tables from the 2000 and 2010 census. They also provide a series of demographic profiles by borough and community district in New York City: A City of Neighborhoods.
Census microdata samples are publicly available from IPUMS, the ACS PUMS site, and the New Census Microdata page. It is useful for NYC researchers to note that Public Use Microdata Areas (PUMAS) closely resemble NYC community districts.