SUMO proteins belong to the Ubiquitin-like protein family, all sharing a common fold and a similar mechanism of conjugation to target polypeptides. SUMO is ubiquitous in all eukaryotes and participates in many crucial pathways. Native SUMO proteins are highly soluble, a property that is exploited in biotechnology. Moreover, SUMO regulates the solubility of aggregation-prone proteins in neurodegenerative disorders. Despite these properties, we show here that human SUMO1, SUMO2, and SUMO3 proteins are at risk of aggregation into amyloid structures if their native conformation is perturbed. Aggregation is mediated by specific regions, which overlap with SUMO functional interfaces, illustrating a competition between function and aggregation. Aggregation of SUMOs might have important physiological implications because disruption of the SUMO pathway is lethal in different organisms. It appears that functional constraints make it difficult to avoid the competition between productive folding and deleterious aggregation in globular proteins, even for essential polypeptides.