We investigate the effects of a remote hydrogen-plasma treatment on Hall parameters as well as on the bound exciton (BEx) photoluminescence (PL) for a variety of ZnO single crystals: bulk air-annealed, Li-doped, and epitaxially grown on sapphire. We present transport and spectroscopic evidence in favor of the hypothesis that hydrogen behaves as a shallow donor rather than a compensating center in ZnO. Specifically, we show that H-plasma-induced increases in 14 luminescence (photon energy: -3.363 eV at 4 K) correlate with increases in free-carrier concentrations from Hall-effect measurements.