Genomic medicine is poised to offer a broad array of new genome-scale screening tests. However, these tests may lead to a phenomenon in which multiple abnormal genomic findings are discovered, analogous to the “incidentalomas” that are often discovered in radiological studies. If practitioners pursue these unexpected genomic findings without thought, there may be disastrous consequences. First, physicians will be overwhelmed by the complexity of pursuing unexpected genomic measurements. Second, patients will be subjected to unnecessary follow-up tests, causing additional morbidity. Third, the cost of genomic medicine will increase substantially with little benefit to patients or physicians (but with great financial benefits to the genomic testing industry), thus throwing the overall societal benefit of genome-based medicine into question. In this article, we discuss the basis for these concerns and suggest several steps that can be taken to help avoid these substantive risks to the practice of genomically personalized medicine.