The interaction of high-velocity neutron stars with the interstellar medium produces bow shock nebulae, in which the relativistic neutron star wind is confined by ram pressure. We present multiwavelength observations of the Guitar Nebula, including narrowband Hα imaging with Hubble Space Telescope (HST) WFPC2, which resolves the head of the bow shock. The HST observations are used to fit for the inclination of the pulsar velocity vector to the line of sight and to determine the combination of spin-down energy loss, velocity, and ambient density that sets the scale of the bow shock. We find that the velocity vector is most likely in the plane of the sky. We use the Guitar Nebula and other observed neutron star bow shocks to test scaling laws for their size and Hα emission, discuss their prevalence, and present criteria for their detectability in targeted searches. The set of Hα bow shocks shows remarkable consistency, in spite of the expected variation in ambient densities and orientations. Together, they support the assumption that a pulsar's spin-down energy losses are carried away by a relativistic wind that is indistinguishable from being isotropic. Comparison of Hα bow shocks with X-ray and nonthermal radio-synchrotron bow shocks produced by neutron stars indicates that the overall shape and scaling is consistent with the same physics. It also appears that nonthermal radio emission and Hα emission are mutually exclusive in the known objects and perhaps in all objects.