Recommendations for laboratories to report incidental findings from genomic tests have stimulated interest in such results. In order to investigate the criteria and processes for assigning the pathogenicity of specific variants and to estimate the frequency of such incidental findings in patients of European and African ancestry, we classified potentially actionable pathogenic single-nucleotide variants (SNVs) in all 4300 European- and 2203 African-ancestry participants sequenced by the NHLBI Exome Sequencing Project (ESP). We considered 112 gene-disease pairs selected by an expert panel as associated with medically actionable genetic disorders that may be undiagnosed in adults. The resulting classifications were compared to classifications from other clinical and research genetic testing laboratories, as well as with in silico pathogenicity scores. Among European-ancestry participants, 30 of 4300 (0.7%) had a pathogenic SNV and six (0.1%) had a disruptive variant that was expected to be pathogenic, whereas 52 (1.2%) had likely pathogenic SNVs. For African-ancestry participants, six of 2203 (0.3%) had a pathogenic SNV and six (0.3%) had an expected pathogenic disruptive variant, whereas 13 (0.6%) had likely pathogenic SNVs. Genomic Evolutionary Rate Profiling mammalian conservation score and the Combined Annotation Dependent Depletion summary score of conservation, substitution, regulation, and other evidence were compared across pathogenicity assignments and appear to have utility in variant classification. This work provides a refined estimate of the burden of adult onset, medically actionable incidental findings expected from exome sequencing, highlights challenges in variant classification, and demonstrates the need for a better curated variant interpretation knowledge base.