In this study, direct-current reactive sputtered ZnO and ZnO1-x based thin film (30 nm and 300 nm in thickness) memristor devices were produced and the effects of oxygen vacancies and thickness on the memristive characteristics were investigated. The oxygen deficiency of the ZnO1-x structure was confirmed by SIMS analyses. The memristive characteristics of both the ZnO and ZnO1-x devices were determined by time dependent current voltage (I-V-t) measurements. The distinctive pinched hysteresis I-V loops of memristors were observed in all the fabricated devices. The typical homogeneous interface and filamentary types of memristive behaviors were compared. In addition, conduction mechanisms, on/off ratios and the compliance current were analyzed. The 30 nm ZnO based devices with native oxygen vacancies showed the best on/off ratio. All of the devices exhibited dominant Schottky emissions and weaker Poole-Frenkel conduction mechanisms. Results suggested that the oxygen deficiency was responsible for the Schottky emission mechanism. Moreover, the compliance currents of the devices were related to the decreasing power consumption as the oxygen vacancies increased.