One of the many new ideas that grew out of the discovery of the quantum Hall effect is the notion of Hall viscosity. The Hall viscosity determines the non-dissipative stresses that develop in a fluid when it flows with a nonuniform velocity. In isotropic, two-dimensional fluids there is a unique Hall viscosity, which can in some cases be related to a topological invariant. In this talk, I will explore what happens when the assumptions of two-dimensionality and isotropy are relaxed. First, I'll show how new non-dissipative viscosity coefficients emerge with only discrete rotational symmetry, and I will connect these with the phenomenology of two-dimensional electron systems. Next, I'll show how cubic symmetry in three dimensions allows for intrinsically three-dimensional Hall viscosity coefficients. Finally, I will show how anisotropic viscosity coefficients can be measured using free surface waves in classical and quantum fluids.