If you have a library membership you may be able to access
The Gale Historical Newspapers collection includes:
Gale Primary Sources
NewsVault
17th and 18th Century Burney Collection
17th and 18th Century Nichols Newspapers Collection
Daily Mail Historical Archive, 1896-2004
The Sunday Times Digital Archive, 1822-2006
British Library Newspapers
19th Century UK Periodicals
19th Century US Newspapers
The Illustrated London News Historical Archive, 1842-2003
The Times Digital Archive
There is also
https://news.google.com/newspapersFor that you really need to know which newspaper you want to look at as as far as I am aware there is no search function.
Otherwise it depends on your sphere of interest. If totally UK then there is the British Newspapers Archive (you can have three free shots there, so you can get a feel for it before you buy.
Or FindMyPast membership (Maybe the more expensive membership option, cant remember) includes access to the BNA
Similarly there is newspapers.com which has North American papers
Also Genealogybank. , mainly US.