A new generation of parton distribution functions with increased precision and quantitative estimates of uncertainties is presented. This work significantly extends previous CTEQ and other global analyses on two fronts: (i) a full treatment of available experimental correlated systematic errors for both new and old data sets; (ii) a systematic and pragmatic treatment of uncertainties of the parton distributions and their physical predictions, using a recently developed eigenvector-basis approach to the hessian method. The new gluon distribution is considerably harder than that of previous standard fits. A number of physics issues, particularly relating to the behavior of the gluon distribution, are addressed in more quantitative terms than before. Extensive results on the uncertainties of parton distributions at various scales, and on parton luminosity functions at the Tevatron RunII and the LHC, are presented. The latter provide the means to quickly estimate the uncertainties of a wide range of physical processes at these high-energy hadron colliders, based on current knowledge of the parton distributions. In particular, the uncertainties on the production cross sections of the W, Z at the Tevatron and the LHC are estimated to be +/-4% and +/-5%, respectively, and that of a light Higgs at the LHC to be +/-5%.