Until the late 80's, when cars were equipped with fuel injectors, if you tried to take off right after you started your car it would spit, sputter, moan, and groan...and might have even stalled on you. Our bodies are a lot like that (especially the older models!) The problem with the car was that the carbureter couldn't get the right mixture of air and fuel until it warmed up. Once again, I won't try to explain all the science behind this, but I understand our bodies to be similar. When one starts running without letting their heart, diaphram, and other muscles adjust to the increase of blood flow and oxygen, their body will protest. Not only will our performance suffer if we don't "warm up", but we are likely to injure ourselves by "pulling a muscle."
In an emergency, our bodies are so wonderfully made that I suppose they can adjust if necessary. However, I definitely believe it is in our best interest to be safe by warming up before we run, and there is really no excuse not to. A few minutes walking or jogging and then a little bouncing up and down ("jumping Jacks" or whatever) should do the trick. If you are going to be sprinting you may even want to add a few faster runs to your warm up before you actually sprint.
The cool down, on the other hand is more of a matter of comfort. Scientific research seems to have debunked the thought that a cool down helps with muscle recovery, but a sudden drop in blood pressure can cause someone to feel light-headed or faint. Walking around a few minutes after a strenuous workout can help you feel better, but there appears to be no reason for a strict "cool-down" portion of a workout.