Semiconductor nanowires are unique as functional building blocks in nanoscale electrical and electromechanical devices. Here, we report on the mechanical properties of ZnO nanowires that range in diameter from 18 to 304 nm. We demonstrate that in contrast to recent reports, Young's modulus is essentially independent of diameter and close to the bulk value, whereas the ultimate strength increases for small diameter wires, and exhibits values up to 40 times that of bulk. The mechanical behavior of ZnO nanowires is well described by a mechanical model of bending and tensile stretching.