Combinatorial laser molecular-beam epitaxy method was employed to fabricate epitaxial ZnO thin films doped with all the 3d transition metal (TM) ions in a high throughput fashion. The solubility behavior of TM ions was discussed from the viewpoints of the ionic radius and valence state. The magneto-optical responses coincident with absorption spectra were observed for Mn- and Co-doped samples. Cathodoluminescence spectra were studied for Cr-, Mn-, Fe-, and Co-doped samples, among which Cr-doped ZnO showed two sharp peaks at 2.97 eV and 3.71 eV, respectively, at the expense of the exciton emission peak of pure ZnO at 3.25 eV. Different magnetoresistance behavior was observed for the samples codoped with n-type carriers. Ferromagnetism was not observed for Cr- to Cu-doped samples down to 3 K.