Meiotic recombinations contribute to genetic diversity by yielding new combinations of alleles. Recently, high-resolution recombination maps were inferred from high-density single-nucleotide polymorphism (SNP) data using linkage disequilibrium (LD) patterns that capture historical recombination events. The use of these maps has been demonstrated by the identification of recombination hotspots and associated motifs, and the discovery that the PRDM9 gene affects the proportion of recombinations occurring at hotspots. However, these maps provide no information about individual or sex differences. Moreover, locus-specific demographic factors like natural selection can bias LD-based estimates of recombination rate. Existing genetic maps based on family data avoid these shortcomings, but their resolution is limited by relatively few meioses and a low density of markers. Here we used genome-wide SNP data from 15,257 parent-offspring pairs to construct the first recombination maps based on directly observed recombinations with a resolution that is effective down to 10 kilobases (kb). Comparing male and female maps reveals that about 15% of hotspots in one sex are specific to that sex. Although male recombinations result in more shuffling of exons within genes, female recombinations generate more new combinations of nearby genes. We discover novel associations between recombination characteristics of individuals and variants in the PRDM9 gene and we identify new recombination hotspots. Comparisons of our maps with two LD-based maps inferred from data of HapMap populations of Utah residents with ancestry from northern and western Europe (CEU) and Yoruba in Ibadan, Nigeria (YRI) reveal population differences previously masked by noise and map differences at regions previously described as targets of natural selection.