The BBC Who Do You Think You Are ? Magazine has announced the launch of the new British Newspaper Archive site.
If you live in Scotland, you can register with the National Library of Scotland to access the Burney collection of 17th and 18th century newspapers from Britain and the colonies; 48 19th century newspapers (though unfortunately, no Borders newspapers); the digital archive of the ephemera collection of the Bodleian Library, Oxford; the Times newspaper (1785 to 1985); the Economist newspaper/magazine (1843-2006).
If you don't live in Scotland then the British Newspaper Archive may be useful.
Use the links to understand more about reasons to search old newspapers and more info about the launch article at the BBC Who Do You Think You Are ? Magazine.
See the comments on 'reasons to search old newspapers' if you're interested in Borders newspapers.