Global efforts to conserve species have been strongly influenced by the heterogeneous distribution of species diversity across the Earth. This is manifest in conservation efforts focused on diversity hotspots. The conservation of genetic diversity within an individual species is an important factor in its survival in the face of environmental changes and disease. Here we show that diversity within species is also distributed unevenly. Using simple genealogical models, we show that genetic distinctiveness has a scale-free power law distribution. This property implies that a disproportionate fraction of the diversity is concentrated in small sub-populations, even when the population is well-mixed. Small groups are of such importance to overall population diversity that even without extrinsic perturbations, there are large fluctuations in diversity owing to extinctions of these small groups. We also show that diversity can be geographically non-uniform--potentially including sharp boundaries between distantly related organisms--without extrinsic causes such as barriers to gene flow or past migration events. We obtained these results by studying the fundamental scaling properties of genealogical trees. Our theoretical results agree with field data from global samples of Pseudomonas bacteria. Contrary to previous studies, our results imply that diversity loss owing to severe extinction events is high, and focusing conservation efforts on highly distinctive groups can save much of the diversity.