Gas solubility in liquids is driven by favorable solute-solvent interactions while being opposed by the entropic cost of creating a molecular-sized cavity of suitable size. We have investigated these contributions to the solvation free energy of small hydrophobic solutes and studied the dependence of the entropy cost of solute insertion on solvent-solvent interactions in cosolvent/water mixtures by means of molecular dynamics simulations. The cosolvents acetone, dimethyl sulfoxide, and sodium chloride were studied. Acetone, which weakly interacts with water relative to hydrogen-bonding interactions in neat water, preferentially binds to hydrophobic solutes thereby raising their solubility. We find that this process is driven by a reduced entropic expense of opening up molecular-sized cavities close to the acetone methyl moieties. Sodium chloride and dimethyl sulfoxide are strongly hydrated, causing entropy to oppose hydrophobic solute insertion even stronger than it does in neat water. In sodium chloride/water the solute is preferentially "wetted" causing it to be "salted-out". Dimethyl sulfoxide methyl moieties bind to the hydrophobic solute. This process, occurring at the expense of entropy, is driven by a favorable solute-solvent energy and causes "salting-in" of the hydrophobic solute.