Members of the family Circoviridae, specifically the genus Circovirus, were thought to infect only vertebrates; however, members of a sister group under the same family, the proposed genus Cyclovirus, have been detected recently in insects. In an effort to explore the diversity of cycloviruses and better understand the evolution of these novel ssDNA viruses, here we present five cycloviruses isolated from three dragonfly species (Orthetrum sabina, Xanthocnemis zealandica and Rhionaeschna multicolor) collected in Australia, New Zealand and the USA, respectively. The genomes of these five viruses share similar genome structure to other cycloviruses, with a circular ~1.7 kb genome and two major bidirectionally transcribed ORFs. The genomic sequence data gathered during this study were combined with all cyclovirus genomes available in public databases to identify conserved motifs and regulatory elements in the intergenic regions, as well as determine diversity and recombinant regions within their genomes. The genomes reported here represent four different cyclovirus species, three of which are novel. Our results confirm that cycloviruses circulate widely in winged-insect populations; in eight different cyclovirus species identified in dragonflies to date, some of these exhibit a broad geographical distribution. Recombination analysis revealed both intra- and inter-species recombination events amongst cycloviruses, including genomes recovered from disparate sources (e.g. goat meat and human faeces). Similar to other well-characterized circular ssDNA viruses, recombination may play an important role in cyclovirus evolution.