Previous compilations of (n, γ ) cross sections of relevance for neutron capture nucleosynthesis in the big bang and in the slow neutron capture process (s process) have been updated to encompass information available up to December 1998; data references include work in process then and published subsequently. The experimental results for nuclei between H and Bi were critically surveyed, renormalized to selected standard cross sections, and condensed into a set of recommended Maxwellian averaged cross sections for a thermal energy of kT = 30 keV. Recent statistical model calculations of the capture cross sections made with the code NON-SMOKER are listed for comparison; these calculated cross sections are adopted in those cases where experimental information is still missing, e.g., for the majority of radioactive nuclei defining the s-process branchings. Maxwellian averages, normalized to our recommended 30 keV averages, were determined for a range of thermal energies between kT = 5 and 100 keV. We have also included the calculated stellar enhancement factors due to thermally populated nuclear states as a function of temperature.