A full description of rarefied gas flows requires the solution of the Boltzmann equation. In the near continuum regime, however, the preferred approach is to solve the Navier-Stokes equation subject to appropriate slip boundary conditions. For gas mixtures, the slip coefficients that enter into the conditions are dependent upon a host of parameters. Thus, one desires simple algebraic expressions for these coefficients that are also quite accurate. We describe in this article a study of the slip problems associated with the flow of binary gas mixtures. Using some general conservation laws, we first augment some previously reported expressions for the velocity and diffusion slips with an expression for the thermal slip and then we reduce all of the expressions to very convenient forms. Next, we report results of numerical computations for some specific gas mixtures using Lennard-Jones potentials and show previously unknown dependencies of the slips on the mixture properties. The new slip coefficients should be of interest in all problems dealing with flows of rarefied gases in the slip regime (for example, in aerosol agglomeration and deposition, flow through capillaries, and flow through porous media), as well as in the technologically important processes of physical and chemical vapor deposition.