Birth, marriage, and death notices might be recorded in your ancestor’s hometown as well as their current residence. Also check newspapers in surrounding towns and counties for news relating to your ancestors. If your ancestor's hometown did not publish their own paper, be sure to search for newspapers printed in the nearest town as they will often include regional news.
There are several online databases where digitized copies of newspapers can be found:
Newspapers.com (available at the Germantown Regional History and Genealogy Center library)
One website, The Ancestor Hunt, deserves special mention. It has a vast listing of links, frequently updated, to online historical newspapers from the United States and all over the world. Other features are lessons on how to perform searches in the newspaper databases and articles relating to newspaper research.
The Tennessee State Library and Archives provides access to The Tennessean (1812 – 2002) to Tennessee residents through TEL. TSLA also has a collection of Tennessee newspapers on microfilm. A list of newspapers available by county can be found here:
Local libraries and history societies are also a good source for newspapers.