RNA homodimerization is important for various physiological processes, including the assembly of membraneless organelles, RNA subcellular localization, and packaging of viral genomes. However, understanding of RNA homodimerization has been hampered by the lack of systematic in vivo detection methods. Here we show that PARIS, COMRADES, and other RNA proximity ligation methods can detect RNA homodimers transcriptome-wide as "overlapping" chimeric reads that contain more than one copy of the same sequence. Analysing published proximity ligation datasets, we show that RNA:RNA homodimers mediated by direct base-pairing interactions are rare across the transcriptome, but highly enriched in specific transcripts, including U8 snoRNA, U2 snRNA and a subset of tRNAs. Analysis of data from virus-infected cells reveals homodimerization of SARS-CoV-2 and Zika genomes, mediated by specific palindromic sequences located within protein-coding regions of N protein in SARS-CoV-2 and NS2A gene in Zika. We speculate that regions of viral genomes involved in homodimerization may constitute effective targets for antiviral therapies.