Monte Carlo simulations are used to trace the critical loci for a number of binary mixtures. In particular, we use grand canonical Monte Carlo (GCMC) simulations with histogram reweighting and mixed-field finite-size scaling to determine the mixture critical lines. Two different classes of criticality are investigated. A mixture of methane and ethane displays type I criticality, exhibiting continuous mixing between the two species across the entire composition range. A methane-water mixture shows type IIIb criticality, with a discontinuity in the critical locus. Quantitative agreement is found between simulation and experimental critical loci for the methane-ethane system using no adjustable parameters for interactions in the mixture. For the water-methane system, we investigate the effect of the combining rules for the intermolecular interaction between the two species on the mixture critical locus. We also investigate several potentials for methane: a nonpolar exponential-6, an octopolar fixed partial charge, and a polarizable fluctuating charge model. Qualitative agreement between simulations and experiments is found for all potentials, but none are able to quantitatively capture the abrupt increase in the critical temperature as methane is added to the system.