The Library of Congress just recently debuted a new feature on their website, the National Jukebox. With this feature, visitors to the Library of Congress website can listen to over ten thousand historic audio recordings. Many of these are classical instrumental and vocal pieces and spoken recordings. A few examples of what you can listen to are: recordings of Presidents Theodore Roosevelt and Woodrow Wilson, many early jazz and folk music recordings, and the first recording of "Rhapsody in Blue" play by George Gershwin.
NPR has an interesting piece on the National Jukebox, which you can listen to and read about here.