The best databases for newspaper research are
Proquest News and Newspapers
Proquest Historical Newspapers
Library of Congress: Chronicling America: Historic American Newspapers
Select Nashville newspapers:
The Tennessean has gone through several name changes
Tennessean: 1972-present
Nashville Tennessean: 1923-1972 (Also in microfilm)
Nashville Tennessean: 1907-1910, 1920-1922
Nashville Tennessean and Nashville American: 1910-1920
Nashville American (precurser to Tennessean): 1894-1910
Daily American (1875-1894)
Nashville Union and American: 1868-1875, 1853-1862
The Nashville Banner was a daily Nashville newspaper from 1876 to 1998. It is mainly not available online. We have 1955-1998 in microfilm on the 6th floor of Central Library. (As well as a microfilm subject index.)
Nashville Public Library's main branch has the Banner on microfilm from 1878 on. NPL maintains a clippings index by which you can search the Banner by topic, from the 1950's on.
Nashville Globe (African-American newspaper) (1906-1918)
Tennessee Tribune (African-American newspaper) (1995-present)
Nashville Scene (1995-present)