RNA-membrane interactions are starting to emerge as an important organizing force in both natural and synthetic biological systems. Notably, RNA molecules were recently discovered to be present on the extracellular surface of living cells, where they mediate intercellular signaling. Furthermore, RNA-membrane interactions influence the efficacy of lipid-based RNA delivery systems. However, the molecular terms driving RNA localization at the membrane remain poorly understood. In this work, we investigate how RNAs bind and interact with phospholipid membranes via all-atom simulations. We find that among RNA nucleobases guanine exhibits the most favorable membrane binding free energy due to extensive hydrogen bond formation. Additionally, we show that intra-RNA base pairing, present in organized RNA structures, significantly hinders RNA-membrane binding. Elucidating the molecular details of RNA-membrane association will importantly contribute to improving the design of RNA-based drugs as well as lipid-based RNA delivery systems and to parsing out RNA transport and localization mechanisms.