CRISPR screens have accelerated the discovery of important cancer vulnerabilities. However, single-gene knockout phenotypes can be masked by redundancy among related genes. Paralogs constitute two-thirds of the human protein-coding genome, so existing methods are likely inadequate for assaying a large portion of gene function. Here, we develop paired guide RNAs for paralog genetic interaction mapping (pgPEN), a pooled CRISPR-Cas9 single- and double-knockout approach targeting more than 2,000 human paralogs. We apply pgPEN to two cell types and discover that 12% of human paralogs exhibit synthetic lethality in at least one context. We recover known synthetic lethal paralogs MEK1/MEK2, important drug targets CDK4/CDK6, and other synthetic lethal pairs including CCNL1/CCNL2. Additionally, we identify ten tumor suppressor paralog pairs whose compound loss promotes cell proliferation. These findings nominate drug targets and suggest that paralog genetic interactions could shape the landscape of positive and negative selection in cancer.