The first song that comes to mind is the one which was mentioned
in an earlier post on this thread. It was written by a high school
teacher in order to get his students to remember some information
about an historical event. (if the information travels through the
ears into the right brain, instead of by reading history with the
left side of the brain, perhaps it is remembered in a different way)
The Battle of New Orleans starts out "In 1814 we took a little trip,
along with Colonel Jackson down the mighty Misiisipp'" the author,
Jimmy Driftwood, used a song that was a traditional fiddle tune,
which may have been familiar to the students, and put words to it.
In this case the tune was "The 8th of January" and you can find more
here: http://www.mudcat.org/thread.cfm?threadid=9661#995482

This is often done by people writing protest songs that they might
want people to sing. Such a song is "Union Maid" by Woodie Guthrie which might be sung by union workers, on a picket line, for instance. The familiar tune used for this one was a song about an Indian Maiden, "Redwing"

This process, of adding new lyrics to old songs is often described
as a "zipper" song, because you "zip" new lyrics into an existing "fabric". Here is a thread where this is discussed.
http://www.mudcat.org/thread.cfm?threadid=15637#141114

I have taught this song to children:
Poost Vzegda Boodyet Solnseh -- sorry for mis spelling,
but it is a song in Russian "May There Always Be Sunshine"
it is said to have been written by a young child.

Tom Paxton, whose song about firefighters on Sept. 11, 2001 (9-11)
is posted above (The Bravest) has a term he uses to describe songs
which deal with news, current events, or which chronicle political
situations "Short Shelf Life songs" these are songs composed to tell
a story or relate situations that may not be long-lasting classic
songs that will stand the test of time, but they serve the purpose
of commenting and informing the listener about today's happenings.
Like the ancient method of passing along news, the travelling Bard
or the town crier who let the people know what was going on.