A checklist of American newspapers in the Columbia University Libraries, from 1704 to the present, arranged by state and city of publication, can be found on the subject guides web page.
It refers to the Periodicals and Microforms Reading Room (call numbers) and/or other libraries where the newspaper is available in print. It also refers to newspaper databases which offer full-text articles online.
Proquest Historical Newspapers has full-text articles from major American newspapers and offers full-page and article images with searchable full-text back to the first issue. Included among others are The New York Times (1851-2005), The Boston Globe (1872-1925) and The Washington Post (1877-1992).
The Periodicals and Microforms Reading Room, located in 401 Butler Library, has current newspapers (i.e. The New York Times) as well as newspapers on microfilm. For more information on the holdings, see the Newspaper Collection page.