Comparisons of DNA polymorphism within species to divergence between species enables the discovery of molecular adaptation in evolutionarily constrained genes as well as the differentiation of weak from strong purifying selection. The extent to which weak negative and positive darwinian selection have driven the molecular evolution of different species varies greatly, with some species, such as Drosophila melanogaster, showing strong evidence of pervasive positive selection, and others, such as the selfing weed Arabidopsis thaliana, showing an excess of deleterious variation within local populations. Here we contrast patterns of coding sequence polymorphism identified by direct sequencing of 39 humans for over 11,000 genes to divergence between humans and chimpanzees, and find strong evidence that natural selection has shaped the recent molecular evolution of our species. Our analysis discovered 304 (9.0%) out of 3,377 potentially informative loci showing evidence of rapid amino acid evolution. Furthermore, 813 (13.5%) out of 6,033 potentially informative loci show a paucity of amino acid differences between humans and chimpanzees, indicating weak negative selection and/or balancing selection operating on mutations at these loci. We find that the distribution of negatively and positively selected genes varies greatly among biological processes and molecular functions, and that some classes, such as transcription factors, show an excess of rapidly evolving genes, whereas others, such as cytoskeletal proteins, show an excess of genes with extensive amino acid polymorphism within humans and yet little amino acid divergence between humans and chimpanzees.