  We show that the tails of the single-point velocity probability distribution
function (PDF) are generally non-Gaussian in developed turbulence. By using
instanton formalism for the Navier-Stokes equation, we establish the relation
between the PDF tails of the velocity and those of the external forcing. In
particular, we show that a Gaussian random force having correlation scale $L$
and correlation time $\tau$ produces velocity PDF tails $\ln{\cal
P}(v)\propto-v^4$ at $v\gg v_{rms}, L/\tau$. For a short-correlated forcing
when $\tau\ll L/v_{rms}$ there is an intermediate asymptotics $\ln {\cal
P}(v)\propto-v^3$ at $L/\tau\gg v\gg v_{rms}$.
