I was fishing around in the 78RPMs and Cylinder Recordings at the Internet Archive, finding wonderful things, when I found some really poorly preserved recordings of really wonderful songs.  Searching for a better copy lead me to the Library of Congress National Jukebox:

National Jukebox historical recordings from the Library of Congress project. You can now play this collection of old music from the early 20th century online. | Library of Congress LOC.gov

Source: National Jukebox LOC.gov

And, if you, like me, end up spending all day listening to old tunes and still can’t get enough, the University of California, Santa Barbara Special Collections Department has a fabulous Cylinder Preservation and Digitization Project.