Axon
An axon, or "nerve fiber," is a long slender projection of a nerve cell or neuron, which conducts electrical impulses away from the neuron's cell body or soma. Axons are in effect the primary transmission lines of the nervous system, and as bundles they help make up nerves. The axons of many neurons are sheathed in myelin.The longest axon in the human body would be those that run from the base of the spine down to the feet, the longest of which probably controls the interosseus muscles which twitch your toes from side to side. That makes that neuron easily the longest cell in the human body.
Compare dendrite.