  We show that long-time, long-distance fluctuations of plane-symmetric
horizons exhibit universal hydrodynamic behavior. By considering classical
fluctuations around black-brane backgrounds, we find both diffusive and shear
modes. The diffusion constant and the shear viscosity are given by simple
formulas, in terms of metric components. For a given metric, the answers can be
interpreted as corresponding kinetic coefficients in the holographically dual
theory. For the near-extremal Dp, M2 and M5 branes, the computed kinetic
coefficients coincide with the results of independent AdS/CFT calculations. In
all the examples, the ratio of shear viscosity to entropy density is equal to
\hbar/(4\pi k_B), suggesting a special meaning of this value.
