Monte Carlo simulations in the Gibbs ensemble were carried out to determine the mutual solubilities for water/n-alkane mixtures over a wide range of temperatures, pressures, and alkane chain lengths. Combinations of the popular, nonpolarizable SPC/E, TIP4P, and TIP4P/2005 water models with the TraPPE united atom model for alkanes are explored to represent these mixtures. Significant deviations from the experimental data are observed for vapor-liquid and liquid-liquid equilibria where the errors in the predicted mole fraction often exceed a factor of 2. Utilizing a scoring metric based on the logarithmic deviation in mole fraction from experimental data, we find that the TIP4P water model outperforms the SPC/E and TIP4P/2005 models in predicting the fluid phase equilibria for water/alkane mixtures. Three models with adjusted Lennard-Jones parameters for water-alkane cross-interactions reflecting departures from the Lorentz-Berthelot combining rules are also investigated. Although a large increase in the well depth can yield a negative Gibbs free energy of transfer for water from the vapor to alkane-rich liquid phases, the overall performance appears to worsen compared to the models using the standard combining rules. Using the standard Lorentz-Berthelot combining rules, the models yield interfacial tensions that deviate by about 10% from the experimental data, but a large increase in the water-alkane cross-interactions leads to a significant underprediction of the interfacial tension.