The more than 1.5 billion people who live in South Asia are correctly viewed not as a single large ethnic group, but as many small endogamous groups. We assembled genome-wide data from over 2,800 individuals from over 275 distinct South Asian groups. We document shared ancestry across groups that correlates with geography, language, and religious affiliation. We characterize the strength of the founder events that gave rise to many of the groups, and identify 14 groups with census sizes of more than a million that descend from founder events significantly stronger than those in Ashkenazi Jews and Finns, both of which have high rates of recessive disease due to founder events. These results highlight a major and under-appreciated opportunity for reducing disease burden among South Asians through the discovery of and testing for recessive disease genes. As a proof-of-principle, we show that it is possible to localize genes for progressive pseudorheumatoid dysplasia and mucopolysaccharidosis type IVA, two recessive diseases prevalent in South India, using the founder event disease gene mapping approach introduced here.