Amyloidoses are a group of diseases associated with the formation of pathological protein fibrils with cross-β structures. Approximately 5–10% of the cases of these diseases are determined by amyloidogenic mutations, as well as by transmission of infectious amyloids (prions) between organisms. The most common group of so-called sporadic amyloidoses is associated with abnormal aggregation of wild-type proteins. Some sporadic amyloidoses are known to be induced only against the background of certain pathologies, but in some cases the cause of amyloidosis is unclear. It is assumed that these diseases often occur by accident. Here we present facts and hypotheses about the association of sporadic amyloidoses with vascular pathologies, trauma, oxidative stress, cancer, metabolic diseases, chronic infections and COVID-19. Generalization of current data shows that all sporadic amyloidoses can be regarded as a secondary event occurring against the background of diseases provoking a cellular stress response. Various factors causing the stress response provoke protein overproduction, a local increase in the concentration or modifications, which contributes to amyloidogenesis. Progress in the treatment of vascular, metabolic and infectious diseases, as well as cancers, should lead to a significant reduction in the risk of sporadic amyloidoses.