We calculate (g-2) of the muon and the QED coupling alpha(M_Z^2), by improving the determination of the hadronic vacuum polarization contributions and their uncertainties. We include the recently re-analysed CMD-2 data on e^+e^- -> pi^+ pi^-. We carefully combine a wide variety of data for the e^+e^- production of hadrons, and obtain the optimum form of R(s) = sigma_had^0(s)/sigma_pt(s), together with its uncertainty. Our results for the hadronic contributions to g-2 of the muon are a_mu^(had,

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... O) = (692.4 +- 5.9_exp +- 2.4_rad) * 10^(-10) and a_mu^(had, NLO) = (-9.8 +- 0.1_exp +- 0.0_rad) * 10^(-10), and for the QED coupling Delta alpha^(5)_had (M_Z^2)= (275.5 +- 1.9_exp +- 1.3_rad) * 10^(-4). These yield (g-2)/2 = 0.00116591763(74), which is about 2.4 sigma below the present world average measurement, and alpha(M_Z^2)^(-1) = 128.954 +- 0.031. We compare our (g-2) value with other predictions and, in particular, make a detailed comparison with the latest determination of (g-2) by Davier et al.