We report on non-polar switching of the resistance between a low and a high resistive state in MgO-based metal-insulator-metal structures. The MgO films were grown by MBE on top of Pt/Si substrates and Pt electrodes were evaporated on top. The obtained resistance ratio is of the order of 10⁸-10⁹, much larger than previously reported values in similar devices. We observe a gradual degradation during consecutive switching events and a significant large dispersion of the voltages at which the resistance switch occurs. The overall behavior of the devices is assigned to a low defect density in these samples. The obtained results suggest that the resistive switching is produced by the formation and disruption of Mg metallic filaments. In order to analyze the influence of interfaces, we also study the effect of adding an intermediate layer of either Al₂O₃ or Mg within the Pt/MgO/Pt structures. The switching performance appears to be enhanced when Al₂O₃ is used.