We study the stochastic dynamics of an ensemble of globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by Gaussian noise. In simulations of the Langevin dynamics we observe that under the increase of noise the mean field proceeds from a steady equilibrium to global oscillations and then, for sufficiently strong noise, back to the equilibrium. In the course of thesetransitions diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed.Details and mechanisms of these noise-induced phenomena are explained in termsof the bifurcations in the deterministic dynamical system which governs, in the thermodynamic limit, the behavior of the cumulants.