Biodiversity hotspots have a prominent role in conservation biology, but it remains controversial to what extent different types of hotspot are congruent. Previous studies were unable to provide a general answer because they used a single biodiversity index, were geographically restricted, compared areas of unequal size or did not quantitatively compare hotspot types. Here we use a new global database on the breeding distribution of all known extant bird species to test for congruence across three types of hotspot. We demonstrate that hotspots of species richness, threat and endemism do not show the same geographical distribution. Only 2.5% of hotspot areas are common to all three aspects of diversity, with over 80% of hotspots being idiosyncratic. More generally, there is a surprisingly low overall congruence of biodiversity indices, with any one index explaining less than 24% of variation in the other indices. These results suggest that, even within a single taxonomic class, different mechanisms are responsible for the origin and maintenance of different aspects of diversity. Consequently, the different types of hotspots also vary greatly in their utility as conservation tools.