  We discuss the realization of mesoscopic phases of dipolar gases relevant to
current experiments with cold polar molecules and Rydberg atoms confined to two
dimensions. We predict the existence of superfluid clusters, mesoscopic
supersolids, and crystals for a small number of trapped particles, with no
counterpart in the homogeneous situation. For certain strengths of the
dipole-dipole interactions, the stabilization of purely {\it non-classical
crystals} by quantum fluctuations is possible. We propose a magnification
scheme to detect the spatial structure of these crystalline phases.
