Little is understood about the occurrence of somatic genomic alterations in normal tissues and their significance in the context of disease. Here, we identified potential somatic copy number alterations (pSCNAs) in apparently normal ovarian tissue and peripheral blood of 423 ovarian cancer patients. There were, on average, two to four pSCNAs per sample detectable at a tissue-level resolution, although some individuals had orders of magnitude more. Accordingly, we estimated the lower bound of the rate of pSCNAs per cell division. Older individuals and BRCA mutation carriers had more pSCNAs than others. pSCNAs significantly overlapped with Alu and G-quadruplexes, and the affected genes were enriched for signaling and regulation. Some of the amplification/deletion hotspots in pan-cancer genomes were hot spots of pSCNAs in normal tissues as well, suggesting that those regions might be inherently unstable. Prevalence of pSCNA in peripheral blood predicted survival, implying that mutations in normal tissues might have consequences for cancer patients.