lots of really good discussions about this parameter, and convergence in general
the value is a good value to look at but you need something to compare it against
the second is you should be looking at converging displacement
Total strain energy is the first thing you should check in a convergence study; something is seriously wrong with your model if it doesn't converge. If your total strain energy has converged, then next you want to check that your displacements converged (as Jared suggested). Both total strain energy and displacement are not, typically, effected by modeling singularities (where as stresses are).
That being said, any other quantities that you're after (stresses, displacement at a given point, forces, etc) should be checked for convergence. Just because a quantity has converged at one location doesn't mean it's converged at all locations (the converse of this statement is true as well).