Understanding the evolutionary history of species is at the core of molecular evolution and is done using several inference methods. The critical issue is to quantify the uncertainty of the inference. The posterior probabilities in Bayesian phylogenetic inference and the bootstrap values in frequentist approaches measure the variability of the estimates due to the sampling of sites from genes and the sampling of genes from genomes. However, they do not measure the uncertainty due to taxon sampling. Taxa that experienced molecular homoplasy, recent selection, a spur of evolution and so forth may disrupt the inference and cause incongruences in the estimated phylogeny. We define a Taxon Influence Index to assess the influence of each taxon on the phylogeny. We found that although most taxa have a weak influence on the phylogeny, a small fraction of influential taxa strongly alter it, even in clades only loosely related to them. We conclude that highly influential taxa should be given special attention and sampling them more thoroughly can lead to more dependable phylogenies.