We present kinematical analyses of 22 Galactic globular clusters using the Hubble Space Telescope proper motion catalogs recently presented in Bellini et al. (Paper I, 2014ApJ...797..115B). For most clusters, this is the first proper-motion study ever performed, and, for many, this is the most detailed kinematic study of any kind. We use cleaned samples of bright stars to determine binned velocity-dispersion and velocity-anisotropy radial profiles and two-dimensional velocity-dispersion spatial maps. Using these profiles, we search for correlations between cluster kinematics and structural properties. The profiles and maps presented here can provide a basis for detailed dynamical modeling of individual globular clusters. Given the quality of the data, this is likely to provide new insights into a range of topics concerning globular cluster mass profiles, structure, and dynamics.