A molecular dynamics simulation study of the local structures and H-bond distribution for water-dimethyl sulfoxide (DMSO) mixtures over the entire composition range is presented. Analysis of several site-site pair distribution functions reveals that two well-defined kinds of aggregates characterize the molecular association between water and DMSO in solution. One of them, already identified through recent neutron diffraction experiments and computer simulations, consists of two water molecules H-bonded to the oxygen atom of a DMSO molecule, such that the angle between the two H-bonds is nearly tetrahedral. The other complex features a central water molecule and two DMSO, making H-bonds to water hydrogens. According to the simulation data, these molecular aggregates coexist with each other in the mixture, but their proportions change with composition. 1DMSO-2water complexes predominate over 2DMSO-1water aggregates for water-rich mixtures (water mole fractions >50%), whereas the opposite is true for DMSO-rich mixtures. The present simulations also seem to indicate that an association between a pair of DMSO molecules through their oxygen atoms is made possible by the formation of the 2DMSO-1water complexes. Implications of the existence of these aggregates to the mobility and other dynamic properties of these mixtures are briefly discussed.