Did you know Google news has an archive of Newspapers from around the world? Have a look at http://news.google.com/newspapers.
Obviously, due to restrictions imposed by the newspapers themselves, you cannot view the most recent editions. However, you may find this useful if you are interested in historical issues. Many of the newspapers have been published since the mid 19th century. Be aware that this is not a complete archive.
If you would like to search a complete archive of newspapers, I recommend you use the newspaper resources available from Senate House Library (SHL). All current staff and students of LSHTM are eligible to join SHL. If you are based in London, just visit SHL with your School ID and they will provide you with a membership card and logon to their electronic resources. If you are based overseas, please email email@example.com for details.