The pompom on a poodle's tail, and the mullet hairstyle are actually practical and remnants from when they were working dogs.
Poodles were bred to hunt in water, the pompom acts as a buoy to show the dog's position when swimming and diving, and the hair on the head and ears is to protect the brain from the cold. Traditionally the rest of the fur, except a few other patches to protect other vital organs, would have been shaved to prevent it absorbing water and making the dog too heavy.