We provide a unified description of thermal equilibria of black hole accretion disks, including the newly-discovered advection-dominated solutions. We classify the solutions on the basis of optical depth and importance of advection cooling. We demonstrate that only four physically distinct topological types of equilibria exist. Two of the types correspond to optically thin and optically thick equilibria, while the other two types are distinguished by whether advection is negligible or dominant. A stable Shakura-Sunyaev disk exists only for accretion rates below a certain maximum. However, there is a critical viscosity parameter , which is a function of radius, such that for advection-dominated solutions exist for all . Even when , the advection-dominated solutions are available for a wide range of except for a gap around the Eddington rate. We therefore suggest that advection-dominated flows may be more common than standard thin disks in black hole systems. For certain ranges of radii and , no stable steady state solution is possible. In these cases, we suggest that limit cycle behavior may occur, leading to variability.