Although Neandertal sequences that persist in the genomes of modern humans have been identified in Eurasians, comparable studies in people whose ancestors hybridized with both Neandertals and Denisovans are lacking. We developed an approach to identify DNA inherited from multiple archaic hominin ancestors and applied it to whole-genome sequences from 1523 geographically diverse individuals, including 35 previously unknown Island Melanesian genomes. In aggregate, we recovered 1.34 gigabases and 303 megabases of the Neandertal and Denisovan genome, respectively. We use these maps of archaic sequences to show that Neandertal admixture occurred multiple times in different non-African populations, characterize genomic regions that are significantly depleted of archaic sequences, and identify signatures of adaptive introgression.