The number of completely searchable pages in the Library of Congress's Chronicling America, Historic American Newspapers, jumped to 6,673,511 pages. This is almost a half a million new pages to search around the country for free. Some of the large commercial subscriptions services claim many more pages of newspapers, but free is nice. The time period covered in the collection is rather limited, from 1836 to 1922, but I suggest that a search in the Library of Congress is always appropriate. You never know what you will find.
You should always be aware of the U.S. Newspaper Directory, 1690 -Present for the most comprehensive list of newspapers published anywhere in America during its entire history of newspaper publishing. The searchable database contains what titles exist for a specific place and time, and how to access them. You can use the options in the search portion of the program to select a particular place and time, using keywords to locate specific titles. Titles number of titles currently listed: 152,145.
You should also search on Google for individual state's newspaper projects. Some of these projects are sponsored by the National Digital Newspaper Program of the Library of Congress. Click here to see a list of states presently participating in the project with links to the participating organizations.