One of the best ways to remove the "abstract" hit point system from D&D is for each player to never know the hit points of his character, but instead have this information tracked by the DM in private.
This kind of system allows the DM a great deal of room to be inventive with the combat system AND keep people from fighting stupidly until their hit points drop below 10. Instead, the DM provides descriptions regarding the degree of an attack and/or the severity of a wound. In fact, red chips can be handed out to illustrate how badly the fight is going.
This allows the other players to show concern over one another as well, when they hear someone has taken a light, heavy, mortal, or fatal wound... after all... no one is going to help a fighter who just took 3 points of damage, but someone may rush to the aid of a character who is nicked just below the eye.
Anyway. It's just an idea.