We report a facile synthesis of zinc oxide (ZnO) nanorod arrays using an optimized, chemical bath deposition method on glass, PET and Si substrates. The morphological and structural properties of the ZnO nanorod arrays were investigated using various techniques such as field emission scanning electron microscopy (FESEM) and X-ray diffraction (XRD) measurements, which revealed the formation of dense ZnO nanorods with a single crystal, hexagonal wurtzite structure. The aspect ratio of the single-crystal ZnO nanorods and the growth rate along the (002) direction was found to be sensitive to the substrate type. The lattice constants and the crystallite size of the fabricated ZnO nanorods were calculated based on the XRD data. The obtained results revealed that the increase in the crystallite size is strongly associated with the growth conditions with a minor dependence on the type of substrate. The Raman spectroscopy measurements confirmed the existence of a compressive stress in the fabricated ZnO nanorods. The obtained results illustrated that the growth of high quality, single-crystal ZnO nanorods can be realized by adjusting the synthesis conditions.