Mosaicism, the presence of subpopulations of cells bearing somatic mutations, is associated with disease and aging and has been detected in diverse tissues, including apparently normal cells adjacent to tumors. To analyze mosaicism on a large scale, we surveyed haplotype-specific somatic copy number alterations (sCNAs) in 1,708 normal-appearing adjacent-to-tumor (NAT) tissue samples from 27 cancer sites and in 7,149 blood samples from The Cancer Genome Atlas. We find substantial variation across tissues in the rate, burden and types of sCNAs, including those spanning entire chromosome arms. We document matching sCNAs in the NAT tissue and the adjacent tumor, suggesting a shared clonal origin, as well as instances in which both NAT tissue and tumor tissue harbor a gain of the same oncogene arising in parallel from distinct parental haplotypes. These results shed light on pan-tissue mutations characteristic of field cancerization, the presence of oncogenic processes adjacent to cancer cells.