  Motivated by recent progress of theory and experiment on the anomalous
magnetic moment of the electron, a_e, we update the hadronic contributions to
a_e. Using our up-to-date compilation of e^+ e^- \to hadrons data, we find the
leading order hadronic contribution a_e^{had,LO,VP} = (1.866 \pm 0.010_{exp}
\pm 0.005_{rad}) \cdot 10^{-12} and the next-to-leading order hadronic
contribution a_e^{had,NLO,VP} = (- 0.2234 \pm 0.0012_{exp} \pm 0.0007_{rad})
\cdot 10^{-12}, where the first and second errors are from the error of the
experimental data and the uncertainty in the treatment of radiative
corrections, respectively. These values are compatible with earlier evaluations
by other groups, but have significantly improved uncertainties due to the more
precise input data used. We also update the leading order hadronic contribution
to the ground state hyperfine splitting of muonium, obtaining \Delta
\nu_{Mu}^{had,VP} = (232.68 \pm 1.25_{exp} \pm 0.72_{rad}) Hz. This value is
consistent with the most precise evaluation in the literature and reduces its
error by a factor of two.
