Three families of RNA viruses, the Coronaviridae, Flaviviridae, and Filoviridae, collectively have great potential to cause epidemic disease in human populations. The current SARS-CoV-2 (Coronaviridae) responsible for the COVID-19 pandemic underscores the lack of effective medications currently available to treat these classes of viral pathogens. Similarly, the Flaviviridae, which includes such viruses as Dengue, West Nile, and Zika, and the Filoviridae, with the Ebola-type viruses, as examples, all lack effective therapeutics. In this review, we present fundamental information concerning the biology of these three virus families, including their genomic makeup, mode of infection of human cells, and key proteins that may offer targeted therapies. Further, we present the natural products and their derivatives that have documented activities to these viral and host proteins, offering hope for future mechanism-based antiviral therapeutics. By arranging these potential protein targets and their natural product inhibitors by target type across these three families of virus, new insights are developed, and crossover treatment strategies are suggested. Hence, natural products, as is the case for other therapeutic areas, continue to be a promising source of structurally diverse new anti-RNA virus therapeutics.