Past demographic changes can produce distortions in patterns of genetic variation that can mimic the appearance of natural selection unless the demographic effects are explicitly removed. Here we fit a detailed model of human demography that incorporates divergence, migration, admixture, and changes in population size to directly sequenced data from 13,400 protein coding genes from 20 European-American and 19 African-American individuals. Based on this demographic model, we use several new and established statistical methods for identifying genes with extreme patterns of polymorphism likely to be caused by Darwinian selection, providing the first genome-wide analysis of allele frequency distributions in humans based on directly sequenced data. The tests are based on observations of excesses of high frequency-derived alleles, excesses of low frequency-derived alleles, and excesses of differences in allele frequencies between populations. We detect numerous new genes with strong evidence of selection, including a number of genes related to psychiatric and other diseases. We also show that microRNA controlled genes evolve under extremely high constraints and are more likely to undergo negative selection than other genes. Furthermore, we show that genes involved in muscle development have been subject to positive selection during recent human history. In accordance with previous studies, we find evidence for negative selection against mutations in genes associated with Mendelian disease and positive selection acting on genes associated with several complex diseases.