The interactions of CO2 with small hydrocarbons and fluorocarbons (CH4, C2H6, CF4, and C2F6) are investigated using the Hartree-Fock and second-order many-body perturbation theory (MP2) methods. Hartree-Fock calculations with flexible basis sets fail to give appreciable binding for any of the four dimers. In contrast, MP2 calculations using flexible basis sets and including corrections for basis-set superposition error give binding energies of the CO2-CH4, CO2-C2H6, CO2-CF4, and CO2-C2F6 clusters ranging from -0.79 to -1.17 kcal/mol. The binding energies for the CO2-hydrocarbon complexes are slightly larger in magnitude than the corresponding CO2-perfluorocarbon clusters.