  We present a new independent evaluation of the hadronic vacuum polarization
contributions a_l{had}(l.o)=(1/2)(g-2)_l{had}(l.o) to the anomalous magnetic
moment (anomaly) of the muon and tau leptons using tau-decays and e+e- data.
The alone theoretical input used for describing the high-energy region not
accessible experimentally is perturbative QCD plus (negligible) additional
effects due to the QCD vacuum condensates. We obtain: a_mu{had}(l.o)=
7020.6(75.6)10^{-11} and a_tau{had}(l.o)= 353.6(3.8)10^{-8}, which we compare
with previous determinations. Our analysis leads to the Standard Model (SM)
prediction: a_mu^{SM}=116~591~846.9(78.9)10^{-11}.Confronting a_mu^{SM} with
the recent BNL measurement leads to a_mu{new}=
a_mu{exp}-a_mu{SM}=176(170)10^{-11}. Combined with the mean existing
determinations of a_mu^{had}(l.o), this leads to the conservative range: -42 <
a_mu{new}10^{11} < 413 at 90% CL, from which we derive conservative lower
bounds on the scales of some new physics. We also update our old predictions of
the SM contributions to a_tau. Including QED to sixth order, higher order
hadronic and electroweak contributions, we obtain a_tau{SM}=117 755(7)10^{-8},
waiting for a future precise measurement of a_tau.
