We argue that the rate density of particle pair production $\Gamma$ in background fields in conformal field theories is determined by the conformal anomaly and related to anomalous trace of the energy-momentum tensor as $\Gamma = (\pi/2) \langle T^\mu_{\ \mu}\rangle$ if the trace is positive (and $\Gamma = 0$ otherwise). This formula perfectly reproduces (presumably, non-Hawking) radiation generated by static gravitational fields in the absence of an event horizon via a new evaporation mechanism suggested recently. Our relation also correctly describes the one-loop Schwinger pair creation in massless (scalar and spinor) quantum electrodynamics. It also accurately points to the Savvidi instability of the gluonic vacuum towards the formation of the chromomagnetic condensate. Photon and neutrino pair production are also discussed.