  We study non-equilibrium polariton superfluids in the optical parametric
oscillator (OPO) regime using a two-component Gross-Pitaevskii equation with
pumping and decay. We identify a regime above OPO threshold, where the system
undergoes spontaneous symmetry breaking and is unstable towards vortex
formation without any driving rotation. Stable vortex solutions differ from
metastable ones; the latter can persist in OPO superfluids but can only be
triggered externally. Both spontaneous and triggered vortices are characterised
by a generalised healing length, specified by the OPO parameters only.
