A recurring question in solar physics concerns the neutralization of electric currents in active regions (ARs), i.e., whether or not the total electric current integrated over a single magnetic polarity of an AR vanishes. This question was recently revisited using three-dimensional (3D) magnetohydrodynamic (MHD) numerical simulations of magnetic flux emergence into the solar atmosphere. Such simulations showed that flux emergence can generate a substantial net current in ARs. Another source of AR currents are photospheric horizontal flows. Regarding the latter, our present aim is to determine the conditions for the occurrence of net vs. neutralized currents. Using 3D MHD simulations, we impose line-tied, quasi-static, photospheric twisting and shearing motions to a bipolar potential magnetic field. We find that such flows: (1) produce both direct and return currents, and (2) can generate force-free magnetic fields with a net current. We demonstrate that neutralized currents are in general produced only in the absence of magnetic shear at the photospheric polarity inversion line - a special condition rarely observed in ARs that produce eruptive flares. Our results thus predict that mostly net currents should be derived from observations of erupting ARs obtained, e.g., with the high-sensitivity Spectro-Polarimeter of the Hinode/Solar Optical Telescope.