  We find that universal three-body physics extends beyond the threshold regime
to non-zero energies. For ultracold atomic gases with a negative two-body
$s$-wave scattering length near a Feshbach resonance, we show the resonant
peaks characteristic of Efimov physics persist in three-body recombination to
higher collision energies. For this and other inelastic processes, we use the
adiabatic hyperspherical representation to derive universal analytical
expressions for their dependence on the scattering length, the collision
energy, and --- for narrow resonances --- the effective range. These
expressions are supported by full numerical solutions of the Schr\"odinger
equation and display log-periodic dependence on energy characteristic of Efimov
physics. This dependence is robust and might be used to experimentally observe
several Efimov features.
