We estimate that there may be up to ∼105 compact objects in the mass range 10−8–10−2 M⊙ per-main-sequence star that are unbound to a host star in the Galaxy. We refer to these objects as nomads; in the literature a subset of these are sometimes called free-floating or rogue planets. Our estimate for the number of Galactic nomads is consistent with a smooth extrapolation of the mass function of unbound objects above the Jupiter-mass scale, the stellar mass density limit and the metallicity of the interstellar medium. We analyse the prospects for detecting nomads via Galactic microlensing. The Wide-Field Infrared Survey Telescope will measure the number of nomads per-main-sequence star greater than the mass of Jupiter to ∼13 per cent, and the corresponding number greater than the mass of Mars to ∼25 per cent. All-sky surveys such as Gaia and Large Synoptic Survey Telescope can identify nomads greater than about the mass of Jupiter. We suggest a dedicated drift scanning telescope that covers approximately 100 deg2 in the Southern hemisphere could identify nomads via microlensing of bright stars with characteristic time-scales of tens to hundreds of seconds.