For foreign historical news, see the guide at http://libguides.princeton.edu/worldnews
A WORD OF CAUTION: Just because a newspaper is digitized, or is well-known in the 21st century, does not mean it was the most prominent or popular newspaper of its day. To learn about the circulation figures of newspapers, you may consult one of the following publications:
N. W. Ayer and Son's American newspaper annual, 1869-1919 (online)
The IMS Ayer directory of publications, 1936-1984 (in print)
Now, if what you need in an American paper published before about 1990, is it in one of the large collections of historical newspapers?
A few historical newspapers have stand-alone online archives. Check the Quick Guide to Major Papers.
Didn't find what you need? Check to see if it has been digitized:
Newspaper digitization projects (ICON: International Coalition on Newspapers)
Wikipedia: list of online newspaper archives
Historical U.S. Newspapers Online (libguide at the University of Pennsylvania, lists papers by state)
If you can’t find digital, you probably can find microfilm. There is a list of newspapers held at Princeton in microfilm, arranged by state, at http://library.princeton.edu/collections/microforms/newspapers/countries/united-states. If we do not have what you need, check Worldcat, then place an Interlibrary Loan request.
If you don’t know what newspapers were published in a particular time/place, check Chronicling America: Newspaper Directory at the Library of Congress. This site also links to many digitized local papers from 1836-1922.
Attention: there are some digital newspaper collections that are not available through an institutional subscription:
If you need information about a paper, try Wikipedia. There are good articles on many historic papers.
If the paper was published after 1990, go to the guide to Current newspapers (Nexis Uni, Newsbank, Factiva).
If you are not a Princeton student, faculty or staff member, you will not able to access most of the fee-based resources listed here from these links. If you are a student somewhere, ask your librarian what your library can provide. If you're a member of the general public, check with your public library, or see the excellent list of papers available for free on the Internet, prepared by Carol Singer at Bowling Green State University: Historical U.S. Newspapers Online
Atlanta Constitution 1868-1984
Arizona Republican 1890-1922
Austin American Statesman 1871-1980
Baltimore Sun 1837-1993
Boston Globe 1872-1988
Chicago Tribune 1849-1996
Christian Science Monitor (1908-2006)
Detroit Free Press (1831-1999)
Harford Courant (1764-1993)
New York Tribune/International Herald Tribune (1841-1962)
New York Times (1851-2015)
Philadelphia Inquirer (1860-2001)
Philadelphia Tribune (1912-2001)
San Francisco Chronicle (1865-1922)
Wall Street Journal (1889-2002)
Washington Post (1877-2002)
Augusta Chronicle (Georgia) 1792+
Charlotte Observer (North Carolina) 1892+
Cleveland Plain-Dealer 1845-1981
Dallas Morning News 1885+
Jersey Journal (Jersey City, New Jersey) 1867-1977, 1999+
Miami Herald 1911+
Mobile Press Register (1970-1983 + more to come)
New Orleans Times-Picayune 1837+
Plain Dealer (Cleveland, Ohio) 1845+
Portland Oregonian 1861+
Richmond Times Dispatch 1903+
Sacramento Bee 1857+
San Francisco Chronicle 1923+
Seattle Daily Times 1895+
Springfield Republican (Massachusetts) 1861-1946, 1988+
State (Columbia, South Carolina) 1891+ Trenton Times 1883+
Washington Evening Star (District of Columbia) 1923-1981