We show that exciton-polariton condensates may exhibit a new fundamental, self-localized nonlinear excitation not seen in other quantum hydrodynamical systems, which takes the form of a dark ring shaped breather. We predict that these structures form spontaneously and remain stable under a combination of uniform resonant and nonresonant forcing. We study single ring dynamics, ring interactions and ring turbulence, and explain how direct experimental observations might be made. We discuss the statistics of ring formation and propose an experimental scheme by which these structures may be exploited to study the smooth cross-over between equilibrium and non-equilibrium critical phase transitions. Finally, we present an alternative mechanism of formation for these topological breathers, in which they circumscribe Gaussian resonant pumps. The observation of a breathing ring soliton would represent the first fundamental breathing soliton within the broad field of quantum hydrodynamics.