Transcription polymerases can exhibit an unusual mode of regenerating certain RNA templates from RNA, yielding systems that can replicate and evolve with RNA as the information carrier. Two classes of pathogenic RNAs (hepatitis delta virus in animals and viroids in plants) are copied by host transcription polymerases. Using in vitro RNA replication by the transcription polymerase of T7 bacteriophage as an experimental model, we identify hundreds of new replicating RNAs, define three mechanistic hallmarks of replication (subterminal de novo initiation, RNA shape-shifting, and interrupted rolling-circle synthesis), and describe emergence from DNA seeds as a mechanism for the origin of novel RNA replicons. These results inform models for the origins and replication of naturally occurring RNA genetic elements and suggest a means by which diverse RNA populations could be propagated as hereditary material in cellular contexts.