[Abridged]: We present a database of structural and dynamical properties for 153 spatially resolved star clusters (50 "young massive clusters" and 103 old globulars) in the Milky Way, the Large and Small Magellanic Clouds, and the Fornax dwarf spheroidal. This database complements and extends others in the literature, such as those of Harris, and Mackey & Gilmore. By fitting a number of models to the clusters' density profiles, we derive various characteristic surface brightnesses and radii; central potentials, velocity dispersions, and escape velocities; total luminosities, masses, and binding energies; phase-space densities and relaxation timescales; and ``kappa-space'' parameters. Population-synthesis models are used to predict intrinsic (B-V) colors, reddenings, and V-band mass-to-light ratios for the same 153 clusters plus another 63 globulars in the Milky Way, and we compare these predictions to the observed quantities where available. These results are intended to serve as the basis for future investigations of structural correlations and the fundamental plane of massive star clusters, including especially comparisons between the systemic properties of young and old clusters. We also address the question of what structural model fits each cluster best, and argue that the extended halos known to characterize many Magellanic Cloud clusters may be examples of the generic envelope structure of self-gravitating star clusters, not just transient features associated strictly with young age.