  (accepted for publication in the Ap.J.) I present a general classification of
self-similar solutions to the equations of gravitational hydrodynamics that
contain many previous results as special cases. For cold flows with spherical
symmetry, the solution space can be classified into several regions of behavior
similar to the Bondi solutions for steady flow. A full description of these
solution is possible, which serves as the asymptotic limit for the general
problem. By applying a shock jump condition, exact general solutions can be
constructed. The isothermal case allows an extra exact integral, and can be
asymptotically analyzed in the presence of finite pressure. These solutions
serve as analytic models for problems such as spherical accretion for star
formation, infall or outflow of gas into galaxies, Lyman alpha cloud dynamics,
etc. Most previous self-similar results are obtained as special cases. The
critical values for a cosmological flow with $\Omega=1$ and $\gamma=4/3$ turn
out to play a special role.
