Historic newspaper provide clues beyond the certificates and courthouse records. They allow us to escape into another world in which our ancestors lived. We see the printed word as they saw it and see their names loom out of the page. Nothing is more exciting than learning an ancestor provided "alms" to a tramper in 1865 who was later arrested for taking the ancestor's coat and hat before leaving the house.
One of the most fantastic web pages is ICON: International Coalition on Newspapers. This contains a listing of newspaper digitization projects, both international collections and United States collections. The bulk of the links to newspapers are shown as free, but there are some liking to subscription databases, such as Ancestry.com, NewspaperArchive.com, Paper of Record and World Newspaper Archive.
I have particularly enjoyed searching the Pennsylvania Civil War Newspapers. The dates are 1855-1871. Imagine stepping back in time to the Civil War era and seeing an ancestor's name in a newspaper. Other examples of links are Suffolk Co., New York Newspapers including the "Long Islander" (Huntington), 1839-1859. Some of the links go directly to state projects, such as the Historic Missouri Newspapers Project or the Georgia Historic Newspapers. There are many more to explore. International newspapers include places like Switzerland, the United Kingdom, Sweden among many more.
It is worth taking some time to browse through the vast number of newspapers that have been digitized. Add some interesting context to your notes about an ancestor ... it's all there for the reading.