Identifying regions of the human genome that have been targets of natural selection will provide important insights into human evolutionary history and may facilitate the identification of complex disease genes. Although the signature that natural selection imparts on DNA sequence variation is difficult to disentangle from the effects of neutral processes such as population demographic history, selective and demographic forces can be distinguished by analyzing multiple loci dispersed throughout the genome. We studied the molecular evolution of 132 genes by comprehensively resequencing them in 24 African-Americans and 23 European-Americans. We developed a rigorous computational approach for taking into account multiple hypothesis tests and demographic history and found that while many apparent selective events can instead be explained by demography, there is also strong evidence for positive or balancing selection at eight genes in the European-American population, but none in the African-American population. Our results suggest that the migration of modern humans out of Africa into new environments was accompanied by genetic adaptations to emergent selective forces. In addition, a region containing four contiguous genes on Chromosome 7 showed striking evidence of a recent selective sweep in European-Americans. More generally, our results have important implications for mapping genes underlying complex human diseases.