Structural variation is widespread in mammalian genomes and is an important cause of disease, but just how abundant and important structural variants (SVs) are in shaping phenotypic variation remains unclear. Without knowing how many SVs there are, and how they arise, it is difficult to discover what they do. Combining experimental with automated analyses, we identified 711,920 SVs at 281,243 sites in the genomes of thirteen classical and four wild-derived inbred mouse strains. The majority of SVs are less than 1 kilobase in size and 98% are deletions or insertions. The breakpoints of 160,000 SVs were mapped to base pair resolution, allowing us to infer that insertion of retrotransposons causes more than half of SVs. Yet, despite their prevalence, SVs are less likely than other sequence variants to cause gene expression or quantitative phenotypic variation. We identified 24 SVs that disrupt coding exons, acting as rare variants of large effect on gene function. One-third of the genes so affected have immunological functions.