Neanderthals were a group of archaic hominins that occupied most of Europe and parts of Western Asia from ~30,000 to 300,000 years ago (KYA). They coexisted with modern humans during part of this time. Previous genetic analyses that compared a draft sequence of the Neanderthal genome with genomes of several modern humans concluded that Neanderthals made a small (1-4%) contribution to the gene pools of all non-African populations. This observation was consistent with a single episode of admixture from Neanderthals into the ancestors of all non-Africans when the two groups coexisted in the Middle East 50-80 KYA. We examined the relationship between Neanderthals and modern humans in greater detail by applying two complementary methods to the published draft Neanderthal genome and an expanded set of high-coverage modern human genome sequences. We find that, consistent with the recent finding of Meyer et al. (2012), Neanderthals contributed more DNA to modern East Asians than to modern Europeans. Furthermore we find that the Maasai of East Africa have a small but significant fraction of Neanderthal DNA. Because our analysis is of several genomic samples from each modern human population considered, we are able to document the extent of variation in Neanderthal ancestry within and among populations. Our results combined with those previously published show that a more complex model of admixture between Neanderthals and modern humans is necessary to account for the different levels of Neanderthal ancestry among human populations. In particular, at least some Neanderthal-modern human admixture must postdate the separation of the ancestors of modern European and modern East Asian populations.