I like a lot of the covers that the Rolling Stones did early on including:
Time Is on My Side (Irma Thomas)
Pain in My Heart (Irma Thomas, Otis Redding)
Here's a good write up about the three versions:
http://www.turnmeondeadman.com/index.php?option=com_content&view=article&id=28&Itemid=38
Turn Me On said:Why he(jake Holmes) chose to do this is puzzling, because he deserves credit for writing "Dazed and Confused."