Chronicling America: Historic American Newspapers
US newspapers 1789-1963, digitised by the Library of Congress. Includes the US Newspaper Directory with information - not text - from a wider date range of US newspapers: 1690 to the present.
Digitised versions of newspapers from around Europe, from the seventeenth century onwards. 10 million pages in total.
International News Archives on the Web
Not updated recently, but may be useful for finding news archives from particular countries.
Trove (Australian newspapers)
Search engine for material in Australian libraries, including newspapers. Tick the Available online box and run your search