The Miami Dolphins have had only one running back turn into a Hall of Famer, making the number one choice on this list easy. Rounding out the other two choices were a bit more difficult, with credence to an old-tier given deliberation along with a newer name to the record books. Here are the three best running backs in the history of the Dolphins franchise. 3. Mercury Morris (1969-75) The first running back on this list to be a part of the repeating Super Bowl champion Dolphins in the early 1970's, Mercury Morris was a three-time Pro Bowler with Miami, spending seven seasons with the franchise after the team selected him out of West Texas A&M University in the third round of the 1969 NFL Draft.