New similarity solutions for free, forced, and mixed convection boundary-layer flow on a permeable horizontal surface embedded in a fluid-saturated porous medium are presented in this paper. Analytical solutions have been obtained for some specific velocity and temperature profiles. The generic case corresponding to a 1/x-type distribution of both the wall temperature and the outer velocity is discussed in detail. In the plane (U, gamma) defined by the mixed convection parameter U and the suction/injection parameter gamma, the existence domain of physical solutions is identified and the main characteristics (wall temperature gradients, decay rates, uniqueness, multiplicity, etc.) of these solutions are investigated systematically.