Static correlation energies (E-stat) are calculated in a range of basis sets for a chemically diverse collection of atoms and molecules. The reliability of a basis set in capturing E-stat is assessed according to the following: mean and maximum absolute deviations from near-exact E-stat estimates, monotonic convergence to the complete basis set limit, and ability to capture E-stat accurately independent of changes in geometry, molecular size, and electronic configuration. Within the polarization and correlation-consistent basis set series, triple-zeta basis sets are the smallest that can reliably capture E-stat. The cc-pVTZ basis set performs particularly well, recovering E-stat to chemical accuracy for all atoms and molecules in our data set. A series of customized basis sets are constructed by stripping polarization functions from, and swapping polarization functions among, existing basis sets. Basis sets without polarization functions are incapable of accurately recovering E-stat. Basis sets with a near-complete set of s, p, and d functions can approach chemical accuracy in maximum absolute error. However, this may be achieved at lower computational cost by using a well balanced triple-zeta basis set including f functions, along with a smaller number of s, p, and d functions. Recommended basis sets for calculating E-stat with increasing accuracy at increasing computational cost are 6-311G(2d,2p), cc-pVTZ, and cc-pVQZ stripped of g functions.