The macroscopic coherence in superconductors supports dissipationless supercurrent which could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions may be expected to enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called superconducting (SC) diode effect. We demonstrate strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish a non-volatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge/surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens door for novel technologies while revealing crucial prerequisites for the search of exotic superconducting states harboring finite-momentum Cooper pairing.