We present the theory of spin relaxation of exciton polaritons treated as a gas of weakly interacting bosons. The model is based on the spin density matrix approach in the Born-Markov approximation. In its framework we have described the spin and energy relaxation of exciton-polaritons in semiconductor microcavities accounting for polariton-polariton and polariton-acoustic phonon scattering. We include various mechanisms of spin relaxation linked with the fine structure of the polaritons. The kinetic equation for time-dependent intensity and polarization of light emitted by the microcavities both at resonant and nonresonant pumping is obtained, The parametric amplification regime, in which the resonant polariton-polariton scattering plays the major role, is specifically analyzed. We show that the polarization plane of the emitted light can rotate as a function of the polarization degree of the pumping light which is a manifestation of the "spin-optronic" effect of self-induced Larmor precession of polariton pseudospins.