We study the Mott transition occurring for bosonic Hubbard models in one, two, and three spatial dimensions by means of a variational wave function benchmarked by Green's function Monte Carlo calculations. We show that a very accurate variational wave function, which is constructed by applying a long-range Jastrow factor to the noninteracting boson ground state, can describe the superfluid-insulator transition in any dimensionality. Moreover, by mapping the quantum averages over such a wave function into the partition function of a classical model, important insights into the insulating phase are uncovered. Finally, the evidence in favor of anomalous scenarios for the Mott transition in two dimensions is reported whenever additional long-range repulsive interactions are added to the Hamiltonian.