Genomic structural variations (SVs) are pervasive in many types of cancers. Characterizing their underlying mechanisms and potential molecular consequences is crucial for understanding the basic biology of tumorigenesis. Here, we engineered a local assembly-based algorithm (laSV) that detects SVs with high accuracy from paired-end high-throughput genomic sequencing data and pinpoints their breakpoints at single base-pair resolution. By applying laSV to 97 tumor-normal paired genomic sequencing datasets across six cancer types produced by The Cancer Genome Atlas Research Network, we discovered that non-allelic homologous recombination is the primary mechanism for generating somatic SVs in acute myeloid leukemia. This finding contrasts with results for the other five types of solid tumors, in which non-homologous end joining and microhomology end joining are the predominant mechanisms. We also found that the genes recursively mutated by single nucleotide alterations differed from the genes recursively mutated by SVs, suggesting that these two types of genetic alterations play different roles during cancer progression. We further characterized how the gene structures of the oncogene JAK1 and the tumor suppressors KDM6A and RB1 are affected by somatic SVs and discussed the potential functional implications of intergenic SVs.