Despite extensive effort to reveal the genetic basis of complex phenotypic variation, studies typically explain only a fraction of trait heritability. It has been hypothesized that individually rare hidden structural variants (SVs) could account for a significant fraction of variation in complex traits. To investigate this hypothesis, we assembled 14 Drosophila melanogaster genomes and systematically identified more than 20,000 euchromatic SVs, of which ~40% are invisible to high specificity short read genotyping approaches. SVs are common in Drosophila genes, with almost one third of diploid individuals harboring an SV in genes larger than 5kb, and nearly a quarter harboring multiple SVs in genes larger than 10kb. We show that SV alleles are rarer than amino acid polymorphisms, implying that they are more strongly deleterious. A number of functionally important genes harbor previously hidden structural variants that likely affect complex phenotypes (e.g., Cyp6g1, Drsl5, Cyp28d1&2, InR, and Gss1&2). Furthermore, SVs are overrepresented in quantitative trait locus candidate genes from eight Drosophila Synthetic Population Resource (DSPR) mapping experiments. We conclude that SVs are pervasive in genomes, are frequently present as heterogeneous allelic series, and can act as rare alleles of large effect.