The time-dependent dielectric breakdown of Co/Al2O3/Co(-Fe) magnetic tunnel junctions is investigated. At voltages larger than 1.2 V, almost immediate breakdown of the junction is observed, leading to a decreased (magneto)resistance. The shorts, which are local hot spots, were visualized by making use of a liquid crystal film on top of the junction. The breakdown voltages of a series of nominally identical tunnel junctions measured in a voltage-ramp experiment are shown to increase with increasing ramp speed. The results are analyzed in the framework of several models for the voltage dependent breakdown probability.