This paper reports a molecular dynamics study of the structure of water around Li+, Na+, K+, Ca++, Ni++and Cl-ions. Jorgensen's TIP4P potential is used for the water-water interaction, and newab initioSCF potentials have been obtained for Ca++/H2O and Ni++/H2O using the recently developed gradient method. In most cases where experimental results are available the positions of the peaks associated with the coordination shells, the ion-water geometries, and the coordination numbers are in satisfactory agreement. However, we believe that more precise neutron measurements of the coordination number of Ni++in dilute solution are needed. The main effects of high pressure on the structure of water around Cl-occur in the second coordination shell. High temperature and high pressure are found to have little effect on the structure around Ca++.