We predict the distinctive three-dimensional space motions of hypervelocity stars (HVSs) and runaway stars moving in a realistic Galactic potential. For nearby stars with distances less than 10 kpc, unbound stars are rare; proper motions alone rarely isolate bound HVSs and runaways from indigenous halo stars. At large distances of 20-100 kpc, unbound HVSs are much more common than runaways; radial velocities easily distinguish both from indigenous halo stars. Comparisons of the predictions with existing observations are encouraging. Although the models fail to match observations of solar-type HVS candidates from SEGUE, they agree well with data for B-type HVS and runaways from other surveys. Complete samples of g <~ 20 stars with Gaia should provide clear tests of formation models for HVSs and runaways and will enable accurate probes of the shape of the Galactic potential.
