While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference has not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal (or flat) for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. There are two related phenomena with respect to topological prior influence in Bayesian phylogenetic analysis: (1) the influence that non-flat clade priors may have on clade posterior probabilities, and (2) the amount of data required to overwhelm such an influence. Regarding the first point, we show that when flat topological priors are stipulated, clade priors are not flat. Specifically, smaller and larger clades have higher prior probability than intermediate sized clades. As such, flat topological priors do not model ignorance when the hypotheses under investigation are clades. In a sample of empirical studies, non-flat clade priors influence clade posterior probabilities in a predictable way; in general intermediate clades have lower posterior probabilities than larger or smaller ones. In the past it has been asserted that the likelihood function will overwhelm any influence of topological priors given sufficient data. However, the amount of data that is sufficient has not been established. In this study, the influence of flat topological priors on clade posteriors is examined with varying numbers of taxa and data simulated using a simple model of substitution.