The Library of Congress is hosting a new website called Chronicling America: Historic American Newspapers. They currently have articles from several newspapers in California, the District of Columbia, Florida, Kentucky, New York, Utah, and Virginia. At the present time they have articles from 1900-1910, but their goal is to expand their coverage to include newspapers from every state from the period from 1836-1922.
You can also look up information on about 140,000 current and historical newspaper titles and see which libraries have them available in some form.