Relatives of cancer patients are at an increased risk of the same (concordant) cancer but whether they are at a risk for different (discordant) cancers is largely unknown - beyond well characterized hereditary cancer syndromes - but would be of major scientific and clinical interest. We therefore decided to resolve the issue by analyzing familial risks when family members were diagnosed with any discordant cancers. We compared the population impact of concordant to discordant familial cancer. The Swedish Family-Cancer Database (FCD) was used to calculate familial relative risks (RRs) for family members of cancer patients, for the 27 most common cancers. Population attributable fractions (PAFs) were estimated for concordant and discordant family histories. Discordant cancers in the family were detected as significant risk factors for the majority of cancers, although the corresponding RRs were modest compared to RRs for concordant cancers. Risks increased with the number of affected family members with the highest RRs for pancreatic (2.31), lung (1.69), kidney (1.98), nervous system (1.79) and thyroid cancers (3.28), when 5 or more family members were diagnosed with discordant cancers. For most cancers, the PAF for discordant family history exceeded that for concordant family history. Our findings suggest that there is an unspecific genetic predisposition to cancer with clinical consequences. We consider it unlikely that shared environmental risk factors could essentially contribute to the risks for diverse discordant cancers, which are likely driven by genetic predisposition. The identification of genes that moderately increase the risk for many cancers will be a challenge.