Two rather closely analogous classes of phenomena — plasma and hydrodynamic ones — are reviewed. Topics covered include: surface waves on an inhomogeneous plasma layer and on an inhomogeneous incompressible flow; the instability of the tangential discontinuity of an inhomogeneous gas flow and the negative mass instability of an electron-beam-carrying plasma; radiative Cherenkov instabilities of an electron beam in a plasma and of a gas flow in a gas; the instability of plasma flows and of incompressible fluid flows with inhomogeneous velocity profiles. Special attention is given to the collisionless damping of plasma surface waves. It is shown that no such damping occurs for surface waves in gas flows.