We have calculated the stability of two of the low-index surfaces known to dominate the morphology of ZnO as a function of stoichiometry. These two surfaces are (10 (1) over bar0) and (11 (2) over bar0). In each case, two terminations only are stable for a significant range of oxygen and hydrogen chemical potential: the pure stoichiometric surface and a surface covered in a monolayer of water. The mode by which the water adsorbs is however different for the two surfaces considered. On the (10 (1) over bar0) surface the close proximity of the water molecules means hydrogen bonding can occur between adjacent chemiabsorbed water molecules and hence there is little difference in the stability of the hydrated and hydroxylated surface, and in fact the most stable surface occurs with a combination of dissociated and undissociated water adsorption. In the case of the (11 (2) over bar0) surface, it is only when full dissociation has occurred that a hydrogen-bonding network can form. Our results also show good agreement between DFT and atomistic simulations, suggesting that potential based methods can usefully be applied to ZnO.