A self-consistent picture of the dynamical evolution of pulsars is developed from an examination of the currently complete sample of pulsar proper motions. The apparent preference for pulsar velocities to be parallel to the galactic plane and the increase in observed transverse velocities with increasing galactic latitude are shown to result from various observational selection effects. The apparent motion of several pulsars toward the galactic plane is converted to an overall expansion of all pulsars from an origin in an extreme Population I distribution by simple vector addition of reasonable radial-velocity components. A strong correlation of velocity magnitude with the product of pulsar period and period derivative is noted, a dynamical value for pulsar magnetic-field decay time is derived, and it is concluded that there are two classes of pulsars distinguished by differences in mean velocity, scale height, and the value of the product of period and period derivative. A model is proposed to explain the origin of the two classes in terms of the presence or absence of a companion star to the supernova that created the neutron star.