Newspaper online archives.

Guardian and Observer newspapers
1821-1975 for the Guardian, and 1900-1975 for the Observer.

Daily Mirror archive
1903 - 2000.

The Times digital archives 1785 - 1985 is operated by Thomson Gale databases and can be accessed through some UK county libraries. Speak to your local librarian.

19th century British Museum newspaper collection
Available through universities, and other subscribing institutions.

Penny Illustrated Paper
Collect Britain website (British Library), 1861-1913 (free).

The Nineteenth-Century Serials Edition (ncse) is a free, online edition of six nineteenth-century periodicals and newspapers.

British Library
Limited archive (free).

The Scotsman
1817 - 1950 (payment or free for Athens users)

The Irish Times
1851 - 2007 (payment)

New Zealand newspapers
1840 - 1915 (free)

Google News archive search
Links to either current news articles on the Google database or numerous other newspaper archives mainly US. Initial search free.

New York Times
Articles between 1851 and 1922 are free. Articles 1923 to 1981 are mainly pay-per-view.