Turbulence in geophysical flows tends to organize itself so that the mean flow remains close to a stability boundary in parameter space. That characteristic suggests self-organized criticality (SOC), a statistical property that has been identified in a range of complex phenomena including earthquakes, forest fires and solar flares. This note explores the relationship between the properties of forced, sheared, stratified turbulence (as found in oceans, atmospheres and other geophysical fluids) and those of SOC. Self-organization to the critical state is demonstrated in a wide range of cases drawn mostly (but not entirely) from in situ observations of ocean turbulence. Turbulent events in the ocean also exhibit a second characteristic associated with SOC: their sizes follow a power-law distribution indicating self-similarity. These results suggest SOC as a new conceptual foundation for the study of geophysical turbulence, an explanation for the mixing efficiency of ocean turbulence and a potential for cross-fertilization with other areas of geophysics.