Circular RNAs (circRNAs) are found across eukaryotes and can function in post-transcriptional gene regulation. Their biogenesis through a circle-forming backsplicing reaction is facilitated by reverse-complementary repetitive sequences promoting pre-mRNA folding. Orthologous genes from which circRNAs arise, overall contain more strongly conserved splice sites and exons than other genes, yet it remains unclear to what extent this conservation reflects purifying selection acting on the circRNAs themselves. Our analyses of circRNA repertoires from five species representing three mammalian lineages (marsupials, eutherians: rodents, primates) reveal that surprisingly few circRNAs arise from orthologous exonic loci across all species. Even the circRNAs from orthologous loci are associated with young, recently active and species-specific transposable elements, rather than with common, ancient transposon integration events. These observations suggest that many circRNAs emerged convergently during evolution - as a byproduct of splicing in orthologs prone to transposon insertion. Overall, our findings argue against widespread functional circRNA conservation.