Today I passed out with my arm tucked beneath my pillow. A couple hours later, I awoke in that same position, and my right arm was dead. From the elbow down, it just felt like rubber. Couldn't move it at all, and it was completely numb. It was really weird to lift my arm up, and watch my hand just flop down like a piece of meat. After a couple minutes, it went back to normal, so I guess there's no lasting damage.
Side note: the second Harry Potter movie had a fairly accurate portrayal of this.