Perspectives on the classification of eukaryotic diversity have changed rapidly in recent years, as the four eukaryotic groups within the five-kingdom classification--plants, animals, fungi, and protists--have been transformed through numerous permutations into the current system of six "supergroups." The intent of the supergroup classification system is to unite microbial and macroscopic eukaryotes based on phylogenetic inference. This supergroup approach is increasing in popularity in the literature and is appearing in introductory biology textbooks. We evaluate the stability and support for the current six-supergroup classification of eukaryotes based on molecular genealogies. We assess three aspects of each supergroup: (1) the stability of its taxonomy, (2) the support for monophyly (single evolutionary origin) in molecular analyses targeting a supergroup, and (3) the support for monophyly when a supergroup is included as an out-group in phylogenetic studies targeting other taxa. Our analysis demonstrates that supergroup taxonomies are unstable and that support for groups varies tremendously, indicating that the current classification scheme of eukaryotes is likely premature. We highlight several trends contributing to the instability and discuss the requirements for establishing robust clades within the eukaryotic tree of life.