The majority of the human genome is transcribed into non-coding (nc)RNAs that lack known biological functions or else are only partially characterized. Numerous characterized ncRNAs function via base pairing with target RNA sequences to direct their biological activities, which include critical roles in RNA processing, modification, turnover, and translation. To define roles for ncRNAs, we have developed a method enabling the global-scale mapping of RNA-RNA duplexes crosslinked in vivo, "LIGation of interacting RNA followed by high-throughput sequencing" (LIGR-seq). Applying this method in human cells reveals a remarkable landscape of RNA-RNA interactions involving all major classes of ncRNA and mRNA. LIGR-seq data reveal unexpected interactions between small nucleolar (sno)RNAs and mRNAs, including those involving the orphan C/D box snoRNA, SNORD83B, that control steady-state levels of its target mRNAs. LIGR-seq thus represents a powerful approach for illuminating the functions of the myriad of uncharacterized RNAs that act via base-pairing interactions.