We have investigated the electrical conduction processes in as-grown and thermally cycled ZnO single crystal as well as as-grown ZnO polycrystalline films over the wide temperature range 20--500 K. In the case of ZnO single crystal between 110 and 500 K, two types of thermal activation conduction processes are observed. This is explained in terms of the existence of both shallow donors and intermediately deep donors which are consecutively excited to the conduction band as the temperature increases. By measuring the resistivity $ρ(T)$ of a given single crystal after repeated thermal cycling in vacuum, we demonstrate that oxygen vacancies play an important role in governing the shallow donor concentrations but leave the activation energy ($≃27±$2 meV) largely intact. In the case of polycrystalline films, two types of thermal activation conduction processes are also observed between $∼$150 and 500 K. Below $∼$150 K, we found an additional conduction process due to the nearest-neighbor-hopping conduction mechanism which takes place in the shallow impurity band. As the temperatures further decreases below $∼$80 K, a crossover to the Mott variable-range-hopping conduction process is observed. Taken together with our previous measurements on $ρ (T)$ of ZnO polycrystalline films in the temperature range 2--100 K [Y. L. Huang {\it et al.}, J. Appl. Phys. \textbf{107}, 063715 (2010)], this work establishes a quite complete picture of the overall electrical conduction mechanisms in the ZnO material from liquid-helium temperatures up to 500 K. ; Comment: 8 pages, 4 figures, 3 tables