Background Chromosomal aneuploidy, that is to say the gain or loss of chromosomes, is the most common abnormality in cancer. While certain aberrations, most commonly translocations, are known to be strongly associated with specific cancers and contribute to their formation, most aberrations appear to be non-specific and arbitrary, and do not have a clear effect. The understanding of chromosomal aneuploidy and its role in tumorigenesis is a fundamental open problem in cancer biology. Results We report on a systematic study of the characteristics of chromosomal aberrations in cancers, using over 15,000 karyotypes and 62 cancer classes in the Mitelman Database. Remarkably, we discovered a very high co-occurrence rate of chromosome gains with other chromosome gains, and of losses with losses. Gains and losses rarely show significant co-occurrence. This finding was consistent across cancer classes and was confirmed on an independent comparative genomic hybridization dataset of cancer samples. The results of our analysis are available for further investigation via an accompanying website. Conclusions The broad generality and the intricate characteristics of the dichotomy of aneuploidy, ranging across numerous tumor classes, are revealed here rigorously for the first time using statistical analyses of large-scale datasets. Our finding suggests that aneuploid cancer cells may use extra chromosome gain or loss events to restore a balance in their altered protein ratios, needed for maintaining their cellular fitness.