  The neutrino energy density of the Universe can be conveniently parametrized
in terms of the so-called effective number of neutrinos, N_nu^eff. This
parameter enters in several cosmological observables. In particular it is an
important input in those numerical codes, like CMBFAST, which are used to study
the Cosmic Microwave Background anisotropy spectrum. By studying the neutrino
decoupling with Boltzmann equations, one can show that this quantity differs
from the number of massless neutrino species for an additional contribution due
to a partial heating of neutrinos during the electron-positron annihilations,
leading to non thermal features in their final distributions. In this paper we
review the different results obtained in the literature and perform a new
analysis which takes into account, in a fully consistent way, the QED
corrections at finite temperature to the photon and e^+- plasma equation of
state. The value found for three massless active neutrinos is N_nu^eff=3.0395,
in perfect agreement with the recommended value used in CMBFAST, N_nu^eff=3.04.
We also discuss the case of additional relativistic relics and massive active
neutrinos.
