Superfluidity, the ability of a quantum fluid to flow without friction, is one of the most spectacular phenomena occurring in degenerate gases of interacting bosons. Since its first discovery in liquid helium-4 (refs 1, 2), superfluidity has been observed in quite different systems, and recent experiments with ultracold trapped atoms have explored the subtle links between superfluidity and Bose-Einstein condensation(3-5). In solid-state systems, it has been anticipated that exciton polaritons in semiconductor microcavities should behave as an unusual quantum fluid(6-8), with unique properties stemming from its intrinsically non-equilibrium nature. This has stimulated the quest for an experimental demonstration of superfluidity effects in polariton systems(9-13). Here, we report clear evidence for superfluid motion of polaritons. Superfluidity is investigated in terms of the Landau criterion and manifests itself as the suppression of scattering from defects when the flow velocity is slower than the speed of sound in the fluid. Moreover, a. Cerenkov-like wake pattern is observed when the flow velocity exceeds the speed of sound. The experimental findings are in quantitative agreement with predictions based on a generalized Gross-Pitaevskii theory(12,13), and establish microcavity polaritons as a system for exploring the rich physics of non-equilibrium quantum fluids.