For a review of these free sites and link aggregation sites, please check out a recent post of mine: Researching Newspapers for Genealogy for Free
One site that I neglected to add to that list is the Google News Archive. Although Google has not increased the size of their collection recently, there still is a ton of material that can be found in Google's offering. While doing a search there you will be presented with both free and pay-for-view results, but there are plenty of free ones. [IMPORTANT NOTE} - when Google presents the search results, when selecting the Free results - it is inaccurate - it fails to include ALL the free ones.
Below is a short video showing how to get the most out of the site. Also included is a tip on how to get a clean snippet of your article that does not include the ever-present highlighted text in either blue or yellow - which is not highly desirable when downloading an article for your own use.
Following this video is a link to all of the hundreds of newspapers that Google has included in their collection.
This is the link to the list of all the newspapers in Google's collection: www.news.google.com/newspapers