Simulation results for liquids composed of linear molecules interacting through dispersion forces and off-center dipoles are presented. Remarkable differences are found on the vapor-liquid equilibrium respect to that of centered dipole molecules. Even more remarkable is the appearance of additional short-range liquid structure at relatively large dipoles and aspect ratios. The existence of dipole dimers is clearly established, and some suggestions allowing for the correspondence between a particular macroscopic phenomenology and a particular dispersion potential function are presented.