Deep level traps detection and characterization in polycrystalline ZnO thin films have been investigated by deep level transient spectroscopy (DLTS) on Pd/ZnO Schottky contacts. Τhe influence of different amounts of incorporated hydrogen in ZnO layers on the creation and evolution of these traps has been studied as well. The films were deposited on n-Si substrates with direct current-sputtering, varying the hydrogen, H, flow rate in the Ar/H sputtering gas, so that the H per volume concentration [H2] was 0%, 20%, 33.3%, 50%, and 66.6%. The Pd/ZnO contacts are more stable and reliable for DLTS characterization than the respective Au/ZnO ones. Four deep electron traps were detected in all samples, referred to as traps A, B, C, and D, with respective activation energies of 0.30, 0.21, 0.47, and 0.54 eV. Another trap, E (0.61 eV), was found in the 50% and 66.6% H2 samples. Traps A and B, which are commonly observed in ZnO, are related to intrinsic defects. Trap C is attributed to surface defects, while trap D may be an extended defect that contains oxygen vacancies. Broad trap E is connected to extended defects. The defects' concentration is higher as the DLTS space-charge region extends closer to the surface. The incorporated hydrogen not only behaves differently depending on the H2 flow rate, but also seems to interact with traps, as it causes a significant reduction in A and B traps' concentrations for [H2] ≤ 33.3%, probably due to the formation of H-VO complexes, and an increase in the other traps' concentrations, in which H participates in, or at least favors their formation for [H2] > 33.3%.