Functional amyloids have been identified in a wide variety of organisms including bacteria, fungi, plants, and vertebrates. Intracellular and extracellular amyloid fibrils of different proteins perform storage, protective, structural, and regulatory functions. The structural organization of amyloid fibrils determines their unique physical and biochemical properties. The formation of these fibrillar structures can provide adaptive advantages that are picked up by natural selection. Despite the great interest in functional and pathological amyloids, questions about the conservatism of the amyloid properties of proteins and the regularities in the appearance of these fibrillar structures in evolution remain almost unexplored. Using bioinformatics approaches and summarizing the data published previously, we have shown that amyloid fibrils performing similar functions in different organisms have been arising repeatedly and independently in the course of evolution. On the other hand, we show that the amyloid properties of a number of bacterial and eukaryotic proteins are evolutionarily conserved. We also discuss the role of protein-based inheritance in the evolution of microorganisms. Considering that missense mutations and the emergence of prions cause the same consequences, we propose the concept that the formation of prions, similarly to mutations, generally causes a negative effect, although it can also lead to adaptations in rare cases. In general, our analysis revealed certain patterns in the emergence and spread of amyloid fibrillar structures in the course of evolution.