The general dispersion relation for electron parametric instabilities of an ultra-intense circularly polarized laser wave is established for arbitrary plasma density. It corresponds to a generalization of the stimulated Raman scattering instability, the relativistic modulational instability, the relativistic filamentation instability, and the two plasmons decay instability. In the relativistic regime the generalized instability is characterized by a wide extent of the unstable region in the wave vector space, with growth rates reaching a fraction of the laser frequency, and a strong harmonic generation. One-dimensional and two-dimensional particle-in-cell simulations confirm these results. In particular a systematic study of the propagation of very intense laser pulses through slabs of plasma of several tens of microns are presented. The instability leads to a rapid longitudinal and transverse electron heating, and to filamentary structures which progressively merge in a nonlinear stage. The heating results in highly energetic electrons with energy of several tens of MeV. Correlatively, a strong attenuation rate of the electromagnetic wave is observed. ©1998 American Institute of Physics.