Archive.org has a lot of great music from the 78rpm era available for download. Here is the seminal old-time country musician Uncle Dave Macon playing and singing Old Dan Tucker (listed here as ‘Old Dam Tucker’). The track was cut in New York City on April 13th, 1925.

UncleDaveMacon-OldDamTucker.mp3

There’s a good Wikipedia page on Old Dan Tucker, including information about its roots in 19th century minstrelsy and a variety of different versions of the tune here: http://en.wikipedia.org/wiki/Old_Dan_Tucker.