Not directly related to the orgin of the song, I do feel the need to mention a rendition of the song by a band called "Frijid Pink." No one has mentioned them and I think that they did the best version of the song. That is my opinion of course. Their version is more like something from Iron Butterfly or Vanilla Fudge (i.e. Acid Rock). Anyway, I prefer their version over the Amimals' or Dylan's.

Check out this link:
http://music.lycos.com/artist/default.asp?QW=Frijid%20Pink