A microscopic statistical mechanical theory of adsorption of supercritical fluids and fluid mixtures on solid surfaces is presented. The fluid density profiles are obtained from the inhomogeneous integral equation theory. The theory is shown to be in excellent agreement with Monte Carlo simulations and to provide substantial improvement over the integral equation theory formulated for homogeneous fluids. A quantitative comparison of theory with the experimental data on the surface excess of supercritical argon and krypton on graphite is presented, and the theory is found to be in good agreement with experiment. In addition, model calculations of adsorption from fluid mixtures are carried out, and the phenomenon of preferential adsorption is discussed.