Microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) based resonators and filters, ranging in frequencies from kHz to GHz, have been proposed. The question of how the stabilities of such resonators scale with dimensions is examined in this paper, with emphasis on the noise characteristics. When the dimensions of a resonator become small, instabilities that are negligible in macro-scale devices become prominent. The effects of fluctuations in temperature, adsorbing/desorbing molecules, outgassing, Brownian motion, Johnson noise, drive power and self-heating, and random vibration are explored. When the device is small, the effects of fluctuations in the numbers of photons, phonons, electrons and adsorbed molecules can all affect the noise characteristics. For all but the random vibration-induced noise, reducing the dimensions increases the noise. At submicron dimensions, especially, the frequency noise due to temperature fluctuations, Johnson noise, and adsorption/desorption are likely to limit the applications of ultra-small resonators.