A systematic study of various, nominally undoped ZnO single crystals, either hydrothermally grown (HTG) or melt grown (MG), has been performed. The crystal quality has been assessed by x-ray diffraction, and a comprehensive estimation of the detailed impurity and hydrogen contents by inductively coupled plasma mass spectrometry and nuclear reaction analysis, respectively, has been made also. High precision positron lifetime experiments show that a single positron lifetime is observed in all crystals investigated, which clusters at 180–182 ps and 165–167 ps for HTG and MG crystals, respectively. Furthermore, hydrogen is detected in all crystals in a bound state with a high concentration (at least 0.3 at. %), whereas the concentrations of other impurities are very small. From ab initio calculations it is suggested that the existence of Zn-vacancy–hydrogen complexes is the most natural explanation for the given experimental facts at present. Furthermore, the distribution of H at a metal/ZnO interface of a MG crystal, and the H content of a HTG crystal upon annealing and time afterward has been monitored, as this is most probably related to the properties of electrical contacts made at ZnO and the instability in p-type conductivity observed at ZnO nanorods in literature. All experimental findings and presented theoretical considerations support the conclusion that various types of Zn-vacancy–hydrogen complexes exist in ZnO and need to be taken into account in future studies, especially for HTG materials.