In addition to the canonical base-pairs comprising the standard Watson-Crick (C:G and U:A) and wobble U:G conformations, an analysis of the base-pair types and conformations in the rRNAs in the high-resolution crystal structures of the Thermus thermophilus 30S and Haloarcula marismortui 50S ribosomal subunits has identified a wide variety of non-canonical base-pair types and conformations. However, the existing nomenclatures do not describe all of the observed non-canonical conformations or describe them with some ambiguity. Thus, a standardized system is required to classify all of these non-canonical conformations appropriately. Here, we propose a new, simple and systematic nomenclature that unambiguously classifies base-pair conformations occurring in base-pairs, base-triples and base-quadruples that are associated with secondary and tertiary interactions. This system is based on the topological arrangement of the two bases and glycosidic bonds in a given base-pair. Base-pairs in the internal positions of regular secondary structure helices usually form with canonical base-pair groups (C:G, U:A, and U:G) and canonical conformations (C:G WC, U:A WC, and U:G Wb). In contrast, non-helical base-pairs outside of regular structure helices usually have non-canonical base-pair groups and conformations. In addition, many non-helical base-pairs are involved in RNA motifs that form a defined set of non-canonical conformations. Thus, each rare non-canonical conformation may be functionally and structurally important. Finally, the topology-based isostericity of base-pair conformations can rationalize base-pair exchanges in the evolution of RNA molecules.