International commissions and national committees for atomic weights (mean relative atomic masses) have recommended regularly updated, best values for these atomic weights as applicable to terrestrial sources of the chemical elements. Presented here is a historically complete listing starting with the values in F. W. Clarke's 1882 recalculation, followed by the recommended values in the annual reports of the American Chemical Society's Atomic Weights Commission. From 1903, an International Commission published such reports and its values (scaled to an atomic weight of 16 for oxygen) are here used in preference to those of national committees of Britain, Germany, Spain, Switzerland, and the U.S.A. We have, however, made scaling adjustments from Ar(16O) to Ar(12C) where not negligible. From 1920, this International Commission constituted itself under the International Union of Pure and Applied Chemistry (IUPAC). Since then, IUPAC has published reports (mostly biennially) listing the recommended atomic weights, which are reproduced here. Since 1979, these values have been called the "standard atomic weights" and, since 1969, all values have been published, with their estimated uncertainties. Few of the earlier values were published with uncertainties. Nevertheless, we assessed such uncertainties on the basis of our understanding of the likely contemporary judgement of the values' reliability. While neglecting remaining uncertainties of 1997 values, we derive "differences" and a retrospective index of reliability of atomic-weight values in relation to assessments of uncertainties at the time of their publication. A striking improvement in reliability appears to have been achieved since the commissions have imposed upon themselves the rule of recording estimated uncertainties from all recognized sources of error.