From the formation of animal flocks to the emergence of coordinated motion in bacterial swarms, populations of motile organisms at all scales display coherent collective motion. This consistent behaviour strongly contrasts with the difference in communication abilities between the individuals. On the basis of this universal feature, it has been proposed that alignment rules at the individual level could solely account for the emergence of unidirectional motion at the group level. This hypothesis has been supported by agent-based simulations. However, more complex collective behaviours have been systematically found in experiments, including the formation of vortices, fluctuating swarms, clustering and swirling. All these (living and man-made) model systems (bacteria, biofilaments and molecular motors, shaken grains and reactive colloids) predominantly rely on actual collisions to generate collective motion. As a result, the potential local alignment rules are entangled with more complex, and often unknown, interactions. The large-scale behaviour of the populations therefore strongly depends on these uncontrolled microscopic couplings, which are extremely challenging to measure and describe theoretically. Here we report that dilute populations of millions of colloidal rolling particles self-organize to achieve coherent motion in a unique direction, with very few density and velocity fluctuations. Quantitatively identifying the microscopic interactions between the rollers allows a theoretical description of this polar-liquid state. Comparison of the theory with experiment suggests that hydrodynamic interactions promote the emergence of collective motion either in the form of a single macroscopic 'flock', at low densities, or in that of a homogenous polar phase, at higher densities. Furthermore, hydrodynamics protects the polar-liquid state from the giant density fluctuations that were hitherto considered the hallmark of populations of self-propelled particles. Our experiments demonstrate that genuine physical interactions at the individual level are sufficient to set homogeneous active populations into stable directed motion.