We study the superfluid and insulating phases of bosons in double-well optical lattices, and focus on the specific example of a two-legged ladder, which is currently accessible in experiments. We obtain the zero-temperature phase diagram using both mean-field and time-evolving block decimation techniques. We find that the mean-field approach describes the correct phase boundaries only when the intrachain hopping is sufficiently small in comparison to the on-site repulsion. We show the dependence of the phase diagram on the interchain hopping or tilt between double wells. We find that the Mott-insulator phase at unit filling exhibits a nonmonotonic behavior as a function of the tilt parameter, producing a reentrant phase transition between Mott insulator and superfluid phases. Finally, we determine the critical point separating the insulating and superfluid phases at commensurate fillings, where the Berezinskii-Kosterlitz-Thouless transition occurs.