Topography is maintained by stress differences within the earth. Depending on the distribution of the stress we classify the support as either local or regional compensation. In general, the stresses implied in a regional compensation scheme are an order of magnitude larger than those corresponding to local isostasy. Gravity anomalies, a measure of the earth's departure from hydrostatic equilibrium, can be used to distinguish between the two compensation mechanisms and thus to estimate the magnitude of deviatoric stress in the crust and upper mantle. Topography created at an oceanic ridge crest or in a major continental orogenic zone appears to be locally compensated. Such features were formed on weak crust incapable of maintaining stress differences much greater than the stress from the applied load. Oceanic volcanoes formed on an already cooled, thickened lithosphere are regionally supported with elastic stresses. Similarly, the broad topographic rise seaward of subduction zones is elastically supported as the lithosphere is bent near the margin. Although the implied stress is to some degree dependent on the rheological model assumed, the gravity anomalies and surface deformation produced by these features demonstrate that the upper 30--40 km of the oceanic lithosphere is capable of regionally supporting stress differences in the 100-MPa range. Given certain conditions of load emplacement, continental crust can also support loads regionally over 100-m.y. time scales, but the effects of erosion only allow an estimate of a lower bound on stress. Data from space probes indicate that the upper layers of other terrestrial planets also support topographic-induced stress differences in excess of 100 MPa.