We have developed arrays of nanomechanical systems (NEMS) by large-scale integration, comprising thousands of individual nanoresonators with densities of up to 6 million NEMS per square centimeter. The individual NEMS devices are electrically coupled using a combined series-parallel configuration that is extremely robust with respect to lithographical defects and mechanical or electrostatic-discharge damage. Given the large number of connected nanoresonators, the arrays are able to handle extremely high input powers (>1 W per array, corresponding to <1 mW per nanoresonator) without excessive heating or deterioration of resonance response. We demonstrate the utility of integrated NEMS arrays as high-performance chemical vapor sensors, detecting a part-per-billion concentration of a chemical warfare simulant within only a 2 s exposure period.