From "Chronicling America" at the Library of Congress, this searchable directory can help you determine what newspapers were published in a specific area and time period, and where copies may be available.
The Catalog of Digital Historical Newspapers (NewspaperCat) facilitates the discovery of online digitized historical newspaper content from newspapers published in the United States and the Caribbean.
Unusual, fragmentary archive of scanned versions of an odd variety of newspapers from different times and places. Most of the historic content is free; limit search results to "Free only."
Search through images of U.S. Newspapers from many states, with dates ranging from 1836-1922. (This is another part of Newspaper Directory site noted above.)
Digital National Newspaper Archives of Mexico. Bulk of material is from the late 1800s and early 1900s. Fully searchable; site and all papers are in Spanish.
England's government "newspaper" specializing in legal notices and official information, published continuously since 1665. Offers free, scanned images of all years, plus search and browse options.
Access to scanned images requires payment. However, the index is handy for locating articles that you can then retrieve from Pfau Library's microfilm copies of the NY Times.