We update our Standard Model predictions for g-2 of the muon and for the hadronic contributions to the running of the QED coupling, Delta alpha_had^(5)(M_Z^2). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2pi channel and from the energy region just below 2 GeV. In particular, for the e+e- -> pi+pi- contribution we include the recent `radiative return' data from KLOE and BaBar. We also include the recent BaBar data on other exclusive channels. We make a detailed study of the effect of replacing the measurements of the inclusive cross section, sigma(e+e- -> hadrons), by the sum of the exclusive channels in the energy interval 1.43 < sqrt{s} < 2 GeV, which includes a QCD sum-rule analysis of this energy region. Our favoured prediction for the muon anomalous magnetic moment is (g-2)/2 = (11659182.8 +- 4.9)*10^(-10) which is 3.3 sigma below the present world-average measurement. We compare our g-2 value with other recent calculations. Our prediction for the QED coupling, obtained via Delta alpha_had^(5)(M_Z^2) = (276.26 +- 1.38)*10^(-4), is alpha(M_Z^2)^(-1) = 128.944 +- 0.019.