We study the superconductor-insulator transition of Bose-Hubbard models with finite-range interactions. Commensurability of the charge distribution with the underlying lattice leads to a richly structured phase diagram. In addition to the lobes of insulating phase characterized by integer fillings, we find-for finite-range interactions-lobes with rational filling factors. At low temperatures we can investigate the phase transition by mapping the model onto a XXZ spin-1/2 Heisenberg model.