Theories of ecological diversification make predictions about the timing and ordering of character state changes through history. These theories are testable by "reconstructing" ancestor states using phylogenetic trees and measurements of contemporary species. Here we use maximum likelihood to estimate and evaluate the accuracy of ancestor reconstructions. We present likelihoods of discrete ancestor states and derive probability distributions for continuous ancestral traits. The methods are applied to several examples: diets of ancestral Darwin's finches; origin of inquilinism in gall wasps; microhabitat partitioning and body size evolution in scrubwrens; digestive enzyme evolution in artiodactyl mammals; origin of a sexually selected male trait, the sword, in platies and swordtails; and evolution of specialization in Anolis lizards. When changes between discrete character states are rare, the maximum-likelihood results are similar to parsimony estimates. In this case the accuracy of estimates is often high, with the exception of some nodes deep in the tree. If change is frequent then reconstructions are highly uncertain, especially of distant ancestors. Ancestor states for continuous traits are typically highly uncertain. We conclude that measures of uncertainty are useful and should always be provided, despite simplistic assumptions about the probabilistic models that underlie them. If uncertainty is too high, reconstruction should be abandoned in favor of approaches that fit different models of trait evolution to species data and phylogenetic trees, taking into account the range of ancestor states permitted by the data.