A methodology implemented to compute photoionization cross sections beyond the electric dipole approximation using Gaussian type orbitals for the initial state and plane waves for the final state is applied to molecules of various sizes. The molecular photoionization cross sections computed for valence molecular orbitals as a function of photon energy present oscillations due to the wave-like nature of both the outgoing photoelectron and of the incoming photon. These oscillations are damped by rotational and vibrational averaging or by performing a k-point summation for the solid state case. For core orbitals, the corrections introduced by going beyond the electric dipole approximation are comparable to the atomic case. For valence orbitals, nondipole corrections to the total photoinization cross sections can reach up to 20% at photon energies above 1 keV. The corrections to the differential cross sections calculated at the magic angle are larger, reaching values between 30% and 50% for all molecules included. Our findings demonstrate that photoelectron spectroscopy, especially angle-resolved, on, e.g., molecules and clusters on surfaces, using high photon energies, must be accompanied by theories that go beyond the electric dipole approximation.