ZnO thin films prepared on various cubic substrates, such as Si, GaAs, GaP, ZnS, CdTe, MgO, NaCl and KCl, by reactive rf sputtering were investigated by using RHEED, TED and TEM. It was found that the crystallinity and epitaxy of ZnO films on (111) A cation faces were better than those on (111) B anion faces. ZnO films on (110) and (100) faces, consisting of both cations and anions showed characteristic crystallographic orientations and surface morphologies. ZnO films on the substrates such as ZnS and CdTe, having about the same ionic character as ZnO, showed epitaxial growth. However those on the substrates such as Si and NaCl, having different ionic character from ZnO, showed poor epitaxy. These results indicate that the ionic characteristics play very important roles in the epitaxial growth of ZnO thin films.