Non-allelic recombination between homologous repetitive elements contributes to evolution and human genetic disorders. Here, we combine short- and long-DNA read sequencing of repeat elements with a new bioinformatics pipeline to show that somatic recombination of Alu and L1 elements is widespread in the human genome. Our analysis uncovers tissue-specific non-allelic homologous recombination hallmarks; moreover, we find that centromeres and cancer-associated genes are enriched for retroelements that may act as recombination hotspots. We compare recombination profiles in human-induced pluripotent stem cells and differentiated neurons and find that the neuron-specific recombination of repeat elements accompanies chromatin changes during cell-fate determination. Finally, we report that somatic recombination profiles are altered in Parkinson’s and Alzheimer’s disease, suggesting a link between retroelement recombination and genomic instability in neurodegeneration. This work highlights a significant contribution of the somatic recombination of repeat elements to genomic diversity in health and disease.