Some newspaper databases collect around a theme, such as those dedicated to African-American newspapers. Others provide a wide range of titles from across the country with varying date ranges, such as America's Historical Newspapers.
If you are looking for a specific newspaper title, or newspapers from a particular city, try using OneSearch first to determine which database might include coverage of the needed resource. FSU may also have the newspaper you need, but only on microfilm.
Contact your subject librarian if you need help navigating the often complicated world of historical newspapers.