So animals have these things called Central Pattern Generators, which are a group of nerve cells (neurons) that function to activate muscle cells. The intersting thing about these Central Pattern Generators is that they do not recieve motor input from the brain. The only thing the brain tells them to do is start and stop, and once started they'll continue until they get the stop command from the brain. These Central Pattern Generators are common in such involuntary activities as walking, chewing, and breathing.

But what's funny is how they discovered this phenomenon of CPG's: two Russian scientists started a cat walking on a treadmill and when it was all good and settled on the treadmill, they chopped its spinal cord. As they hypothesized, the hind legs amazingly kept on walking on the treadmill. I really wish I could see a video of this experiment.