Under violent astrophysical conditions, intense fluxes of neutrinos candrive a novel class of plasma instabilities: the electroweak versions ofthe standard electron- and photon-driven forward scatteringinstabilities. Employing the relativistic kinetic equations for theneutrinos interacting with a plasma via the weak interactionforce, weexplore the different collective plasma instabilities driven byneutrinos. We examine theanomalous energy transfer between the neutrinos and the backgroundplasma via excitation of electron plasma waves (neutrino streaminginstability), and the generation of quasi-static B fields(electroweak Weibel instability). The relevance of the electroweakplasma instabilities for the extreme conditions occurring in the leptonera of the early universe, supernovae II, and gamma ray bursters ispointed out. The impact on type II supernovae dynamics is examined, andestimates for the energy deposited via collective mechanisms behind theoutgoing shock are presented. We show that electroweak plasmainstabilities might play an important role in the re-energization of thestalled shock in SNe II.