Results of many calculations of the MP2 correlation energies for ground states of closed-shell atoms (referred to as MP2/CA energies) are presented and studied. Special attention is paid to laying down rules which govern the dependence on the nuclear charge (Zdependence) and on the number of electrons (Ndependence) of (a) the partial wave (PW) increments to the second-order pair energies, (b) the second-order pair energies, and (c) the configurational pair energies. It has been found that these energy increments disclose many regularities useful from both the physical and computational points of view. Some of the MP2/CA increments are quasi-transferable between similar systems. The results obtained are used as a starting point for an extensive discussion of the methodological significance of MP2/CA studies, and for indicating various actual and potential areas of application of the MP2/CA approach in many-electron theory.