Looks like the U.S. Newspaper Program http://www.neh.gov/projects/usnp.html is starting to pay off. I have always liked Colorado & Utah's free digital newspapers. Now it looks like you will be able to access the digital papers from The Library of Congress website. Now in BETA, Chronicling America: Historic American Newspapers http://www.loc.gov/chroniclingamerica/index.html only covers 25 papers in 7 states between 1900-1910, but this will be an interesting project to watch.
The Chronicling America: Historic American Newspapers website will also let you find information about newspapers published in the United States from 1690 to the present in the Chronicling America Directory & tell you where you can find them.
Hoping to find the original digital newspaper websites for a larger database I was able to find these:
Good site for finding world wide digital newspapers:
The International Coalition on Newspapers-http://icon.crl.edu/digitization.htm