Complex animals display bilaterally asymmetric motor behavior, or "motor handedness," often revealed by preferential use of limbs on one side. For example, use of right limbs is dominant in a strong majority of humans. While the mechanisms that establish bilateral asymmetry in motor function are unknown in humans, they appear to be distinct from those for other handedness asymmetries, including bilateral visceral organ asymmetry, brain laterality, and ocular dominance. We report here that a simple, genetically homogeneous animal comprised of only ~1000 somatic cells, the nematode C. elegans, also shows a distinct motor handedness preference: on a population basis, males show a pronounced right-hand turning bias during mating. The handedness bias persists through much of adult lifespan, suggesting that, as in more complex animals, it is an intrinsic trait of each individual, which can differ from the population mean. Our observations imply that the laterality of motor handedness preference in C. elegans is driven by epigenetic factors rather than by genetic variation. The preference for right-hand turns is also seen in animals with mirror-reversed anatomical handedness and is not attributable to stochastic asymmetric loss of male sensory rays that occurs by programmed cell death. As with C. elegans, we also observed a substantial handedness bias, though not necessarily the same preference in direction, in several gonochoristic Caenorhabditis species. These findings indicate that the independence of bilaterally asymmetric motor dominance from overall anatomical asymmetry, and a population-level tendency away from ambidexterity, occur even in simple invertebrates, suggesting that these may be common features of bilaterian metazoans.