Universal, giant and nonvolatile resistive switching is demonstrated for oxide tunnel junctions with ferroelectric PbZr0.2Ti0.8O3, ferroelectric BaTiO3, and paraelectric SrTiO3 tunnel barriers. The effects are caused by reversible migration of oxygen vacancies between the tunnel barrier and bottom La2/3Sr1/3MnO3 electrode. The switching process, which is driven by large electric fields, is efficient down to a temperature of 5 K.