It is shown that low Reynolds number fluid flows can cause suspended particles to respond as though they were in an equilibrium system with an effective potential. This general result follows naturally from the fact that different methods of moving particles in viscous fluids give rise to very different long-range flows. Two examples are discussed: electrophoretic ‘levitation’ of a heavy charged sphere, for which a hydrodynamic ‘pseudo-potential’ can be written in closed form, and quasi-two-dimensional crystals of like-charged colloidal spheres which form near charged walls, whose apparent attraction arises not from a force but from persistent fluid flows.