Four major US papers--Atlanta Constitution (1868-1939), Boston Globe (1872-1924), Chicago Tribue (1849-1986), NYTimes (1851-2004)--are available through Proquest. To access, from the HCHS home page, mouse over "library" and then "edatabases" and then choose (the slightly misleadingly named) link: "NYT Historical". This database should be available for students to use from home with their username and password, however problems with access have been reported. Let me know what people's experiences are and I'll work with the technology department to see if they can be fixed.
The Brooklyn Daily Eagle (1841-1902) has been digitized by the Brooklyn Public Library and is available here:
The Library of Congress has a beta site with several state newspapers (including from New York) available from 1900-1910 here:
Freedom's Journal: The "first African-American owned and operated newspaper published in the United States. The Journal was published weekly in New York City from 1827 to 1829. All 103 issues have been digitized and placed into Adobe Acrobat format."
Two other places for newspaper links: