Human cells have twenty-three pairs of chromosomes. In cancer, however, genes can be amplified in chromosomes or in circular extrachromosomal DNA (ecDNA), although the frequency and functional importance of ecDNA are not understood. We performed whole-genome sequencing, structural modelling and cytogenetic analyses of 17 different cancer types, including analysis of the structure and function of chromosomes during metaphase of 2,572 dividing cells, and developed a software package called ECdetect to conduct unbiased, integrated ecDNA detection and analysis. Here we show that ecDNA was found in nearly half of human cancers; its frequency varied by tumour type, but it was almost never found in normal cells. Driver oncogenes were amplified most commonly in ecDNA, thereby increasing transcript level. Mathematical modelling predicted that ecDNA amplification would increase oncogene copy number and intratumoural heterogeneity more effectively than chromosomal amplification. We validated these predictions by quantitative analyses of cancer samples. The results presented here suggest that ecDNA contributes to accelerated evolution in cancer.