The OPLS set of intermolecular potential functions has been extended to cover ammonium and carboxylate ions. The functions are shown to provide good descriptions of the structure and energetics for isolated ion-water complexes in comparison with results of ab initio molecular orbital calculations. However, the principal testing involved Monte Carlo statistical mechanics simulations of dilute aqueous solutions of NH4+, CH3NH3+, (CH3)4N+, HCOO-, and CH3COO- at 25°C and 1 atm. The computed results are in accord with experimental heats of solution and also provide detailed insights into the hydration of the ions. In particular, NH4+ and CH3NH3+ are found to participate in 5 and 4 strong hydrogen bonds with water molecules, respectively, while the carboxylate ions have about 7 strongly bound water molecules in the first hydration layer. The hydration of (CH3)4N+ is less specific and involves weaker interactions with 20-30 water molecules in the first solvation shell. The success of the study supports the viability of the potential functions for use in computer simulations of complex biochemical and interfacial systems.