In that video, there are some new links, which I thought I should replicate here, so here are the links to free sites, as well as some sites that contain even more links.
Below is the video, and below that are the links.
These are the links to the free sites and link aggregation sites:
Historic American Newspapers - Library of Congress
Penn Libraries - Historical Newspapers Online
Lawson Research Services (Leslie Lawson) - Newspaper Links of Old
Online Historical Newspapers Website (Miriam Robbins)
Wikipedia Online Newspaper Archives