Below are links to websites with collections of 19th century newspapers.
Great Lakes Region History Pages on Century Past
Great Lakes History Periodicals: Newspapers
Kenneth R. Marks, who created this website, made a page for each U.S. State with links to vintage online newspapers, indicating which are free of charge. There are also pages for:
-Jewish American Newspapers
For more online collections of U.S. historical newspapers, see: Free Newspaper Archives
Washington: Library of Congress
This Library of Congress directory of U.S. Newspapers lists a huge number of past newspapers, when and where they were published, and where they can be found now. Part of the newspapers are digitized on this site.
Google offers archived copies of numerous U.S. newspapers arranged alphabetically. Late-19th century issues are available online for many of these, and a few newspapers offer mid-19th century issues.
University of Pennsylvania
This Penn Library site is a collection of links to archived online U.S. newspapers, grouped by state.