Tropical America (the Neotropics) harbours more plant species than any other region on Earth. The contribution of rare species to this diversity has been recently recognised, but their spatial distribution remains poorly understood. Here, we use all collection records of angiosperms from the Global Biodiversity Information Facility to delineate Neotropical bioregions, and to identify putatively rare species within the Neotropics and the Amazonian rainforest. We analyse the spatial distribution of these species and validate the results on a largely independent dataset based on vegetation plots from the Amazon Tree Diversity Network. We find that rare species are homogeneously distributed through most parts of the lowland Neotropics and Amazonia, but more concentrated in highlands. The second collection of any rare species is most often found in the close vicinity of the first, but in 20% of cases they are more than 580 km apart. We also find cross‐taxonomic patterns of disjunct distributions within the Andes, the Atlantic forest in eastern Brazil, and between Amazonia and the Atlantic forest, but no clear disjunction patterns within lowland areas. These results suggest that a considerable proportion of rare plant species have surprisingly large distribution ranges, and that collections of rare species across most of the lowland Neotropics, and in particular in Amazonia, show no clear directionality. The second record of many rare species may be found virtually anywhere, urging the need for intensifying and broadening biological sampling.