Here are some major NY titles. You can find a spreadsheet listing all known digital NY titles to the right.
New York Times, 1851-2009, via Proquest Historical Newspapers.
America's Historical Newspapers has 157 titles of New York Newspapers, covering 29 cities. Copies range in date from 1733-1850 (though most are early 19th century). Six titles for Ithaca, from 1817 to 1837, are included. (The same titles are available through the subscription product GenealogyBank.com.)
Paper of Record has 3 N.Y. titles: Mackenzie's Gazette and the New York Examiner from New York City, and the Volunteer from Rochester. Years covered range from 1838-1842.
The Syracuse Post-Standard has made over 4 million pages of Syracuse newspapers from 1809 to 2008 available through the NewspaperArchive.com product (to which Cornell subscribes).
Hobart and WIlliam Smith Colleges has made the full-text of several Geneva-area newspapers freely available and is indexing others. Currently The Expositor (1806-1809), Geneva Gazette (1809-1812 and misc. issues 1824-1826), and Geneva Palladium from 1821-1825 and 1826-1828, with misc. issues from 1816-1820, are online.
The Monroe County Public Library System in Rochester, NY has created a Rochester Area Historic Newspapers Collection with digitized copies of 19th and early 20th century newspapers with a Rochester area connection. 12 titles are available, including Frederick Douglass' Paper and The North Star (both of which are also available in text form from Accessible Archives), the Liberal Advocate, and the Rights of Man.
Other New York abolitionist newspapers are available. Freedom's Journal, published in New York City from 1827 to 1829, was the first African-American owned and operated newspaper published in the US. All 103 issues have been digitized by the Wisconsin Historical Society. Transcribed text is available from Accessible Archives, either online or on CD in the Library.
Accessible Archives' African-American Newspapers: The 19th Century, available online and as a CD in the Libray, includes 4 New York papers: Freedom's Journal (available above as well), The Colored American (Weekly Advocate), Frederick Douglass Paper, and The North Star. Accessible Archives offers transcriptions of the orignal text.
The Cornell University Library has digitized The Friend of Man, an early reform era and abolitionist paper published in Central New York from 1836-1842.
The Suffolk County Public Library makes 7 titles ranging in date from 1839 to 1960 available in its Suffolk Historic Newspaper project.
The Old Fulton NY Post Card WebSite has scanned and indexed over 6 million pages of central and northern New York newspapers. A browsable list of titles, which range in date from 1806 to 2007, is available. There are 8 titles from Ithaca, ranging in date from 1846 to 1922.
Three New York City newspapers - The Evening World, The New-York Tribune, and The Sun are included in the Chronicling America project. The Tribune is available from 1880-1910; the other two from 1900-1910.
The Brooklyn Public Library has available the Brooklyn Daily Eagle for 1841-1902.
The Poughkeepsie Journal is being digitized by Footnote.com, a subscription product. Scattered years are available now, but Footnote promises to digitize the run. Cornell does not have an institutional subscription, but individual memberships are relatively inexpensive.
The Empty Closet is one of the oldest continuously published LGBT papers in the United States. It was begun at the University of Rochester and later transferred to the Gay Alliance of the Genesee Valley (GAGV). Issues from 1971 to 2001 are available online and searchable.
Don't forget to look for New York content in the National Newspaper collections as well.