Results from molecular dynamics simulations are reported, describing self-organization in solutions of charged dendrimer molecules upon variation of the strength of the electrostatic interactions, in the presence of explicit solvent and counterions. Systems of two sizes bearing different surface charge densities are studied at constant temperature and volume conditions. It is found that a systematic variation of Bjerrum length triggers a mechanism associated with counterion spatial correlations, which drives the systems from an amorphous liquidlike arrangement to an ordered state bearing the symmetry of a cubic phase. The role of dendrimer interpenetration, trapping of counterions, and solvent depletion in the ordering process is also explored. As this study employs a description which takes into account all the principal internal degrees of freedom of dendrimer molecules, the conclusions drawn are expected to offer a fair description of the behavior of realistic systems bearing similar dendritic topology.