Tests of models of melt generation and mantle source variations beneath mid-ocean ridges require a definitive set of mid-ocean ridge basalt (MORB) compositions corrected for shallow-level processes. Here we provide such a dataset, with both single sample and segment means for 241 segments from every ocean basin, which span the entire range of spreading rate, axial depth, and MORB chemical composition. Particular attention is paid to methods of fractionation correction. Values corrected to 8 wt % MgO are robust as they are within the range of the data. Extrapolation to equilibrium with mantle olivine is a non-unique procedure that is critically dependent on the MgO content where plagioclase first appears. MORB data, trace element ratios and calculated liquid lines of descent provide consistent evidence that plagioclase fractionation primarily occurs between 8 and 9 wt % MgO, with the exception of hydrous magmas mainly from back-arc segments. Varying the MgO content of plagioclase appearance over large ranges does not produce the observed systematics at 8 wt % MgO, but may contribute to the spread of the data. Data were evaluated individually for each segment to ensure reliable fractionation correction, and segment means are reported normalized both to MgO of 8 wt % and also to a constant Mg/(Mg + Fe) in equilibrium with Fo sub(90) olivine. Both sets of corrected compositions show large variations in Na sub(2)O and FeO, good correlations with segment depth, and systematic relationships among the major elements. A particularly good correlation exists between Al sub(90) and Fe sub(90). These new data are not in agreement with the presentation of Niu & O'Hara (Journal of Petrology 49, 633-664, 2008), whose results relied on an inaccurate fractionation correction procedure, which led them to large errors for high- and low-FeO magmas. The entire dataset is provided in both raw and normalized form so as to have a uniform basis for future evaluations. The new data compilation permits tests of competing models for the primary causes of variations in MORB parental magmas: variations in mantle composition, mantle temperature, reactive crystallization or lithospheric thickness. The principal component of chemical variation among segment mean compositions is remarkably consistent with variations in mantle temperature of some 200 degree C beneath global ocean ridges. Comparisons with experimental data, pMELTS and other calculations show that variations in mantle fertility at constant mantle potential temperature produce trends that are largely orthogonal to the observations. At the same time, there is clear evidence for mantle major element heterogeneity beneath and around some hotspots and beneath back-arc basins. Super slow-spreading ridges display a characteristic chemical signature of elevated Na sub(90) and Al sub(90) and lowered Si sub(90) relative to faster-spreading ridges. If this signature were produced by reactive crystallization, Si sub(90) should be higher rather than lower in these environments owing to the thicker lithosphere and lower temperatures of mantle-melt reaction. Instead, the data are consistent with lower extents of mantle melting beneath a thicker lithosphere. Hence, variations in extent of melting appear to be the dominant control on the major element compositions of MORB parental magmas. Trace elements, in contrast, require a large component of mantle heterogeneity, apparent in the factor of 50 variation in K sub(90). Such variations do not correlate with the other major elements, showing that major element and trace element (and isotope) heterogeneity reflect different processes. This supports the model of movement of low-degree melts for the creation of trace element and isotope mantle heterogeneity, and is inconsistent with large variations in the amount of recycled crust in most ocean ridge mantle sources.