Each human genome includes de novo mutations that arose during gametogenesis. While these germline mutations represent a fundamental source of new genetic diversity, they can also create deleterious alleles that impact fitness. Whereas the rate and patterns of point mutations in the human germline are now well understood, far less is known about the frequency and features that impact de novo structural variants (dnSVs). We report a family-based study of germline mutations among 9,599 human genomes from 33 multigenerational CEPH-Utah families and 2,384 families from the Simons Foundation Autism Research Initiative. We find that de novo structural mutations detected by alignment-based, short-read WGS occur at an overall rate of at least 0.160 events per genome in unaffected individuals, and we observe a significantly higher rate (0.206 per genome) in ASD-affected individuals. In both probands and unaffected samples, nearly 73% of de novo structural mutations arose in paternal gametes, and we predict most de novo structural mutations to be caused by mutational mechanisms that do not require sequence homology. After multiple testing correction, we did not observe a statistically significant correlation between parental age and the rate of de novo structural variation in offspring. These results highlight that a spectrum of mutational mechanisms contribute to germline structural mutations and that these mechanisms most likely have markedly different rates and selective pressures than those leading to point mutations.