Ion-π interactions between the face of a molecular π-system and a cation or anion are among the strongest noncovalent interactions known, with applications throughout biochemistry and structural biology, molecular recognition and host-guest chemistry, as well as enzyme kinetics and organocatalysis. In this work, we examine the competing notions of selectivity and flexibility in this class of noncovalent interactions by investigating how certain π-systems can be promiscuous ion-π binders with the versatility to form favorable cation- and anion-π complexes. We focus our efforts on a detailed theoretical case study of the DNA/RNA nucleobases by first demonstrating that these π-systems are promiscuous ion-π binders with the biologically relevant Li+/Na+ cations and F-/Cl- anions via benchmark-quality quantum-mechanical binding energy curves computed at the CCSD(T)/CBS level of theory. Using a symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis, we explore the different physicochemical driving forces underlying the formation of cation- and anion-π complexes, as well as the crucial role played by charge penetration effects in determining the nontrivial (and often counterintuitive) electrostatics in anion-π systems. In doing so, a unified view of these rather distinct noncovalent binding motifs emerges with the finding that both cation- and anion-π complexes are strongly stabilized by an essentially ring-independent potential that can only be overcome by substantially unfavorable electrostatics. This work furnishes a more comprehensive explanation for decades of observed correlations between the equilibrium binding energy and the electrostatic potential above the ring and provides new insight into the nature of selectivity and flexibility in this important class of noncovalent interactions. Quite interestingly, the analysis presented herein demonstrates that π-systems have an inherent propensity to bind both cations and anions, thereby implying that promiscuous ion-π binding is not an exotic property of the nucleobases and should be common in nature.