Genetic networks are characterized by extensive buffering. During tumour evolution, disruption of these functional redundancies can create de novo vulnerabilities that are specific to cancer cells. In this regard, paralog genes are of particular interest, as the loss of one paralog gene can render tumour cells dependent on a remaining paralog. To systematically identify cancer-relevant paralog dependencies, we searched for candidate dependencies using CRISPR screens and publicly available loss-of-function datasets. Our analysis revealed >2,000 potential candidate dependencies, several of which were subsequently experimentally validated. We provide evidence that DNAJC15-DNAJC19, FAM50A-FAM50B and RPP25-RPP25L are novel cancer relevant paralog dependencies. Importantly, our analysis also revealed unexpected redundancies between sex chromosome genes. We show that chrX- and chrY- encoded paralogs, as exemplified by ZFX-ZFY, DDX3X-DDX3Y and EIF1AX-EIF1AY, are functionally linked so that tumour cell lines from male patients with Y-chromosome loss become exquisitely dependent on the chrX-encoded gene. We therefore propose genetic redundancies between chrX- and chrY- encoded paralogs as a general therapeutic strategy for human tumours that have lost the Y-chromosome.