Structural variations of DNA greater than 1 kilobase in size account for most bases that vary among human genomes, but are still relatively under-ascertained. Here we use tiling oligonucleotide microarrays, comprising 42 million probes, to generate a comprehensive map of 11,700 copy number variations (CNVs) greater than 443 base pairs, of which most (8,599) have been validated independently. For 4,978 of these CNVs, we generated reference genotypes from 450 individuals of European, African or East Asian ancestry. The predominant mutational mechanisms differ among CNV size classes. Retrotransposition has duplicated and inserted some coding and non-coding DNA segments randomly around the genome. Furthermore, by correlation with known trait-associated single nucleotide polymorphisms (SNPs), we identified 30 loci with CNVs that are candidates for influencing disease susceptibility. Despite this, having assessed the completeness of our map and the patterns of linkage disequilibrium between CNVs and SNPs, we conclude that, for complex traits, the heritability void left by genome-wide association studies will not be accounted for by common CNVs.