Several reports proposed that the extraordinary dominance of the SAR11 bacterial clade in ocean ecosystems could be a consequence of unusual mechanisms of resistance to bacteriophage infection, including `cryptic escape' through reduced cell size and/or K-strategist defence specialism. Alternatively, the evolution of high surface-to-volume ratios coupled with minimal genomes containing high-affinity transporters enables unusually efficient metabolism for oxidizing dissolved organic matter in the world's oceans that could support vast population sizes despite phage susceptibility. These ideas are important for understanding plankton ecology because they emphasize the potentially important role of top-down mechanisms in predation, thus determining the size of SAR11 populations and their concomitant role in biogeochemical cycling. Here we report the isolation of diverse SAR11 viruses belonging to two virus families in culture, for which we propose the name `pelagiphage', after their host. Notably, the pelagiphage genomes were highly represented in marine viral metagenomes, demonstrating their importance in nature. One of the new phages, HTVC010P, represents a new podovirus subfamily more abundant than any seen previously, in all data sets tested, and may represent one of the most abundant virus subfamilies in the biosphere. This discovery disproves the theory that SAR11 cells are immune to viral predation and is consistent with the interpretation that the success of this highly abundant microbial clade is the result of successfully evolved adaptation to resource competition.