An arrow to the arm will certainly not chop it off, and, when using swords and axes, limbs should only be lopped after a few hits. This makes sense when you start fighting enemies with plated armor.
EDIT: I think we may want to think about impairments, such as those found in Fallout 3. For example, when my character encounters a grenade, his leg goes limp. I hope at least THIS mechanic makes it into Skyrim, as it isn't gorey but still realistic.