Aqueous solutions of 1:1 strong electrolytes are considered to be the prototype for complete ionic dissociation. Nonetheless, clustering of strong 1:1 electrolytes has been widely reported in all atom molecular dynamics simulations, and their presence is indirectly implicated in a diverse range of experimental results. Is there a physical basis for nonidealities such as ion pairing and cluster formation in aqueous solutions of strong 1:1 electrolytes? We attempt to answer this question by direct comparison of results from detailed molecular dynamics simulations to experimentally observed properties of 1:1 electrolytes. We report the analysis of a series of lengthy molecular dynamics simulations of alkali-halide solutions carried out over a wide range of physiologically relevant concentrations using explicit representations of water molecules. We find evidence for pronounced nonideal behavior of ions at all concentrations in the form of ion pairs and clusters which are in rapid equilibrium with dissociated ions. The phenomenology for ion pairing seen in these simulations is congruent with the multistep scheme proposed by Eigen and Tamm based on data from ultrasonic absorption experiments. For a given electrolyte, we show that the dependence of cluster populations on concentration can be described through a single set of equilibrium constants. We assess the accuracy of calculated ion pairing constants by favorable comparison to estimates obtained by Fuoss and co-workers and based on conductometric experiments. Ion pairs and clusters form on length scales where the size of individual water molecules is as important as the hard core radius of ions. Ion pairing results as a balance between the favorable Coulomb interactions and the unfavorable partial desolvation of ions needed to form a pair.