As a consequence of strong collective behavior, the microscopic dynamics of the one-component plasma (OCP) differs significantly from that of ordinary liquids. We show that, when particle caging dominates, the OCP transport coefficients nevertheless satisfy universal laws satisfied by dense ordinary fluids: the Stokes-Einstein relation, the Arrhenius law of viscosity, and several excess-entropy scaling relations. These results extend to long-range interaction potentials, the unifying description of atomic transport in condensed matter.