I've noticed a couple of teams--like the mid-00's Packers and Seahawks--where it didn't seem to actually matter who their running back was. Even their third and fourth string backs would perform well. This is when I started to suspect that a team's blocking--the offensive line and fullback--made more of a difference to the running game than the running back. Not that you don't need a good running back, but that the ability to run fast enough and go through the holes created by the blockers are dime-a-dozen type talents and it's not difficult to find someone to fit in that role.

If this is true, than probably the single most important thing that actually hinges on the running back himself is fumble rate. (On the other hand, Adrian Peterson seems like one of the rare running backs whose actual talent extends beyond, say, an Ahman Green or Shaun Alexander.)