Wavelength-scale, high Q-factor photonic crystal cavities have emerged as a platform of choice for on-chip manipulation of optical signals, with applications ranging from low-power optical signal processing and cavity quantum electrodynamics, to biochemical sensing. Many of these applications, however, are limited by the fabrication tolerances and the inability to precisely control the resonant wavelength of fabricated structures. Various techniques for post-fabrication wavelength trimming and dynamical wavelength control -- using, for example, thermal effects, free carrier injection, low temperature gas condensation, and immersion in fluids -- have been explored. However, these methods are often limited by small tuning ranges, high power consumption, or the inability to tune continuously or reversibly. In this letter, by combining nano-electro-mechanical systems (NEMS) and nanophotonics, we demonstrate reconfigurable photonic crystal nanobeam cavities that can be continuously and dynamically tuned using electrostatic forces. A tuning of ~10 nm has been demonstrated with less than 6 V of external bias and negligible steady-state power consumption.