Possible planetary objects have now been discovered orbiting nine different main-sequence stars. These companion objects (some of which might actually be brown dwarfs) all have a mass at least half that of Jupiter, and are therefore unlikely to be hospitable to Earth-like life: jovian planets and brown dwarfs support neither a solid nor a liquid surface near which organisms might dwell. Here we argue that rocky moons orbiting these companions could be habitable if the planet-moon system orbits the parent star within the so-called 'habitable zone', where life-supporting liquid water could be present. The companions to the stars 16 Cygni B and 47 Ursae Majoris might satisfy this criterion. Such a moon would, however, need to be large enough (>0.12 Earth masses) to retain a substantial and long-lived atmosphere, and would also need to possess a strong magnetic field in order to prevent its atmosphere from being sputtered away by the constant bombardment of energetic ions from the planet's magnetosphere.