Conduction processes in as-grown and annealed n-type ZnO crystals have been studied by means of Hall-effect measurements and X-ray photoelectron spectroscopy (XPS). For temperatures above approximately 50 K, the conductance is dominated by electrons in the bulk of the crystal, whereas below that temperature, surface conductance becomes more important. As the crystals are annealed in flowing N2 gas, the surface sheet carrier concentration increases, and concomitantly, the OH-bond peak in the XPS spectrum becomes a larger fraction of the total O peak. Conversely, either O2-plasma annealing or electron-beam irradiation produces a decrease in the surface conductance and the OH fraction. Thus, H-related donors are likely the cause of the surface conductance.