The propagation of intense picosecond laser pulses in air in the presence of strong nonlinear self-action effects and air ionization is investigated experimentally and numerically. The model used for numerical analysis is based on the nonlinear propagator for the optical field coupled to the rate equations for the production of various ionic species and plasma temperature. Our results show that the phenomenon of plasma-driven intensity clamping, which has been paramount in femtosecond laser filamentation, holds for picosecond pulses. Furthermore, the temporal pulse distortions in the picosecond regime are limited and the pulse fluence is also clamped. In focused propagation geometry, a unique feature of picosecond filamentation is the production of a broad, fully ionized air channel, continuous both longitudinally and transversely, which may be instrumental for many applications including laser-guided electrical breakdown of air, channeling microwave beams and air lasing.