In this paper we treat the preionization problem in shocks over the velocity range 10<v_s_<1500km/s in a self-consistent manner. We identify four distinct classes of solutions controlled by the value of the shock-precursor parameter, {Psi}=Q/v_s_, where Q is the ionization parameter of the UV photons escaping upstream. This parameter determines both the temperature and the degree of ionization of the gas entering the shock. In increasing velocity, the shock solution regimes are cold neutral precursors (v_s_<~40km/s), warm neutral precursors (40<~v_s_<~75km/s), warm partly ionized precursors (75<~v_s_<~120km/s), and fast shocks in which the preshock gas is in photoionization equilibrium and is fully ionized. The main effect of a magnetic field is to push these velocity ranges to higher values and to limit the postshock compression. In order to facilitate comparison with observations of shocks, we provide a number of convenient scaling relationships for parameters, such as postshock temperature, compression factors, cooling lengths, and H{beta} and X-ray luminosity.