Its been called "Ragdoll Physics" and its pretty awesome. If you don't believe me, play Rainbow Six 3 for Xbox (not sure if the computer version incorporates it). You almost never see the same position twice and although its not perfect it leads to some pretty awesome visuals...Oh I think I have a link to a movie:
Now with real-time skeletal animation you could cause your character to crumple down against a wall or physically react to his/her environment which would be cool, but most don't. Just shoot someone next to a wall and watch what happens. They normally end up lying down in the same position as their other dead companions with one head or both legs sticking through the wall.
There is a recent game that uses skeletal animation albeit it need a bit of refining since the characters tend to end up in some very...shall we say 'acrobatic'...positions.