The seafloor is characterized by numerous seamounts and oceanic islands which are mainly volcanic in origin. Relatively few of these features (<~0.1%), however, have been dated, and so little is known about their tectonic setting. One parameter that is sensitive to whether a seamount formed on, near, or far from a mid-ocean ridge is the elastic thickness, Te, which is a proxy for the long-term strength of the lithosphere. Most previous studies are based on using the bathymetry to calculate the gravity anomaly for different values of Te and then comparing the calculated and observed gravity anomaly. The problem with such an approach is that bathymetry data are usually limited to single-beam echo sounder data acquired along a ship track and these data are too sparse to define seamount shape. We therefore use the satellite-derived gravity anomaly to predict the bathymetry for different values of Te. By comparing the predicted bathymetry to actual shipboard soundings in the vicinity of each locality in the Wessel global seamount database, we have obtained 9758 Te estimates from a wide range of submarine volcanic features in the Pacific, Indian, and Atlantic oceans. Comparisons where there are previous estimates show that bathymetric prediction is a robust way to estimate Te and its upper and lower bounds. Te at sites where there is both a sample and crustal age show considerable scatter, however, and there is no simple relationship between Te and age. Nevertheless, we are able to tentatively assign a tectonic setting to each Te estimate. The most striking results are in the Pacific Ocean where a broad swath of "on-ridge" volcanism extends from the Foundation seamounts and Ducie Island/Easter Island ridge in the southeast, across the equator, to the Shatsky and Hess rises in the northwest. Interspersed among the on-ridge volcanism are "flank ridge" and "off-ridge" features. The Indian and Atlantic oceans also show a mix of tectonic settings. Off-ridge volcanism dominates in the eastern North Atlantic and northeast Indian oceans, while flank ridge volcanism dominates the northeastern Indian and western south Atlantic oceans. We have been unable to assign the flank ridge and off-ridge estimates an age, but the on-ridge estimates generally reflect, we believe, the age of the underlying oceanic crust. We estimate the volume of on-ridge volcanism to be ~1.1 ¿ 106 km3 which implies a mean seamount addition rate of ~0.007 km3 yr-1. Rates appear to have varied through geological time, reaching their peak during the Late/Early Cretaceous and then declining to the present-day.