Counting individual RNA or DNA molecules is difficult because they are hard to copy quantitatively for detection. To overcome this limitation, we applied unique molecular identifiers (UMIs), which make each molecule in a population distinct, to genome-scale human karyotyping and mRNA sequencing in Drosophila melanogaster. Use of this method can improve accuracy of almost any next-generation sequencing method, including chromatin immunoprecipitation-sequencing, genome assembly, diagnostics and manufacturing-process control and monitoring.