Flux creep in disordered superconductors may be governed by quantum tunneling of Abrikosov vortices rather than by thermal activation processes. The expectation is that in the quantum tunneling regime the creep rate would be temperature independent. This assumes that the parameters describing the pinning potential and other aspects of the superconducting films are temperature independent. In the case of extremely thin superconducting films the coherence length retains its temperature dependence well into the quantum tunneling regime, leading to an unusual temperature dependence of the electrical resistance in this regime. This has been observed in ultrathin superconducting films of Pb, Al, and Bi. In low magnetic fields, at low temperatures, sheet resistances vary with temperature as R≈R0 exp(T/T0), where T0 and R0 are constants.