We report 428 new redshifts for galaxies in the vicinity of twelve rich clusters. The clusters we have observed-A85, A569, A957, A1069, A1185, A1750, A1991, A2063, A2440, A2589, A2593, and A2657-exhibit a wide range of optical and x-ray properties, from extremely luminous x-ray emitters with apparently dense central regions, to clusters which exhibit a bimodal or clumpy appearance in their galaxy and x-ray surface brightness distributions. Several of the clusters (and subclusters) contain dominant galaxies with multiple nuclei embedded in an extended luminous halo. We discuss the velocity distributions for each of these clusters, and obtain dynamical mass estimates. Application of a simple two-body dynamical model has implications for several of the clusters studied. The subclusters in A569 are likely to be gravitationally bound to one another and presently coming together prior to the final relaxation of the system. The formal result of the two-body analysis for A957 indicates that the system is not gravitationally bound, but the uncertainty in the radial velocity difference between the subclusters allows for bound solutions with equal probability. The cluster A1069, which appears to be a double cluster in a previously published map of the galaxy distribution, is shown to be a clear case of foreground/background superposition. The two main subclusters in A1750 are apparently gravitationally bound to one another and infalling, although unbound solutions are also allowed with roughly a 10% probability. The cluster A2440 is shown to be comprised of two primary subclusters which are gravitationally bound to each other, and in the process of infall. The clusters A2589 and A2593 apparently form a bound pair which are presently expanding away from one another prior to turn around, although unbound solutions are also allowed with somewhat lower likelihood. We consider our measurements of the relative velocities of brightest cluster member galaxies (usually morphologically classified as D or cD) with respect to the remaining galaxies in each cluster, and argue that when significantly large differences are observed this is strong evidence for the existence of substructure within the cluster. Based on the significant velocity offsets of the D/cD galaxies in the clusters A85, A1185, A2063, and A2589, we expect that the substructure will be revealed in these clusters when more complete spatial and velocity data become available. The subcluster A957W may also harbor unresolved substructure. Finally, we consider the distribution of measured velocity scales for clusters in our sample, and show that velocity dispersions derived when substructure is present (but ignored) can be high by a factor as large as 2. We conclude that the limiting dispersions of rich clusters is still not well constrained.