Anfinsen's thermodynamic hypothesis does not explicitly take into account the possibility of protein aggregation. Here, we introduce a cyclic-perturbation approach to prove that not only the native state but also soluble aggregates of most proteins can be highly populated under mild, physiologically relevant conditions, even at very low concentration. Surprisingly, these aggregates are not necessarily amyloid in nature and are usually not observed in bioactive proteins due to the extremely low kinetic flux from the native state toward a region of the chemical-potential landscape encoding aggregates. We first illustrate this concept for the representative model protein apomyoglobin at room temperature and no denaturant-and demonstrate kinetic trapping of the native state relative to at least two different types of soluble, predominantly nonamyloid aggregates. The concentration and temperature dependence of aggregation confirm the above scenario. Extension of our analysis to the Escherichia coli proteome shows that the majority of the soluble bacterial proteome is also kinetically trapped in the nonaggregated state. Hence, the existence and low kinetic accessibility of large aggregates at room temperature and pH 6-7 is a general phenomenon. We also show that the average critical protein concentration for aggregation of most of the bacterial proteome is extremely small, much lower than the typical cellular protein concentration. Hence, the thermodynamic driving force for protein aggregation is large even if aggregation does not usually occur in healthy cells due to kinetic trapping. A broader view of Anfinsen's thermodynamic hypothesis encompassing all protein states, including aggregates, is necessary to understand the behavior of proteins in their natural environment.