The nature of evolutionary changes recorded by the fossil record has long been controversial, with particular disagreement concerning the relative frequency of gradual change versus stasis within lineages. Here, I present a large-scale, statistical survey of evolutionary mode in fossil lineages. Over 250 sequences of evolving traits were fit by using maximum likelihood to three evolutionary models: directional change, random walk, and stasis. Evolution in these traits was rarely directional; in only 5% of fossil sequences was directional evolution the most strongly supported of the three modes of change. The remaining 95% of sequences were divided nearly equally between random walks and stasis. Variables related to body size were significantly less likely than shape traits to experience stasis. This finding is in accord with previous suggestions that size may be more evolutionarily labile than shape and is consistent with some but not all of the mechanisms proposed to explain evolutionary stasis. In general, similar evolutionary patterns are observed across other variables, such as clade membership and temporal resolution, but there is some evidence that directional change in planktonic organisms is more frequent than in benthic organisms. The rarity with which directional evolution was observed in this study corroborates a key claim of punctuated equilibria and suggests that truly directional evolution is infrequent or, perhaps more importantly, of short enough duration so as to rarely register in paleontological sampling.