Genome-wide patterns of variation across individuals provide a powerful source of data for uncovering the history of migration, range expansion, and adaptation of the human species. However, high-resolution surveys of variation in genotype, haplotype and copy number have generally focused on a small number of population groups. Here we report the analysis of high-quality genotypes at 525,910 single-nucleotide polymorphisms (SNPs) and 396 copy-number-variable loci in a worldwide sample of 29 populations. Analysis of SNP genotypes yields strongly supported fine-scale inferences about population structure. Increasing linkage disequilibrium is observed with increasing geographic distance from Africa, as expected under a serial founder effect for the out-of-Africa spread of human populations. New approaches for haplotype analysis produce inferences about population structure that complement results based on unphased SNPs. Despite a difference from SNPs in the frequency spectrum of the copy-number variants (CNVs) detected--including a comparatively large number of CNVs in previously unexamined populations from Oceania and the Americas--the global distribution of CNVs largely accords with population structure analyses for SNP data sets of similar size. Our results produce new inferences about inter-population variation, support the utility of CNVs in human population-genetic research, and serve as a genomic resource for human-genetic studies in diverse worldwide populations.