Combinations of anti-cancer drugs can overcome resistance and provide new treatments^1,2. The number of possible drug combinations vastly exceeds what could be tested clinically. Efforts to systematically identify active combinations and the tissues and molecular contexts in which they are most effective could accelerate the development of combination treatments. Here we evaluate the potency and efficacy of 2,025 clinically relevant two-drug combinations, generating a dataset encompassing 125 molecularly characterized breast, colorectal and pancreatic cancer cell lines. We show that synergy between drugs is rare and highly context-dependent, and that combinations of targeted agents are most likely to be synergistic. We incorporate multi-omic molecular features to identify combination biomarkers and specify synergistic drug combinations and their active contexts, including in basal-like breast cancer, and microsatellite-stable or KRAS-mutant colon cancer. Our results show that irinotecan and CHEK1 inhibition have synergistic effects in microsatellite-stable or KRAS–TP53 double-mutant colon cancer cells, leading to apoptosis and suppression of tumour xenograft growth. This study identifies clinically relevant effective drug combinations in distinct molecular subpopulations and is a resource to guide rational efforts to develop combinatorial drug treatments.