Prions derived from the prion protein (PrP) were first characterized as infectious agents that transmit pathology between individuals. However, the majority of cases of neurodegeneration caused by PrP prions occur sporadically. Proteins that self-assemble as cross-beta sheet amyloids are a defining pathological feature of infectious prion disorders and all major age-associated neurodegenerative diseases. In fact, multiple non-infectious proteins exhibit properties of template-driven self-assembly that are strikingly similar to PrP. Evidence suggests that like PrP, many proteins form aggregates that propagate between cells and convert cognate monomer into ordered assemblies. We now recognize that numerous proteins assemble into macromolecular complexes as part of normal physiology, some of which are self-amplifying. This review highlights similarities among infectious and non-infectious neurodegenerative diseases associated with prions, emphasizing the normal and pathogenic roles of higher-order protein assemblies. We propose that studies of the structural and cellular biology of pathological versus physiological aggregates will be mutually informative.