Intrinsic connectivity, measured using resting-state fMRI, has emerged as a fundamental tool in the study of the human brain. However, due to practical limitations, many studies do not collect enough resting-state data to generate reliable measures of intrinsic connectivity necessary for studying individual differences. Here we present general functional connectivity (GFC) as a method for leveraging shared features across resting-state and task fMRI and demonstrate in the Human Connectome Project and the Dunedin Study that GFC offers better test-retest reliability than intrinsic connectivity estimated from the same amount of resting-state data alone. Furthermore, at equivalent scan lengths, GFC displayed higher estimates of heritability than resting-state functional connectivity. We also found that predictions of cognitive ability from GFC generalized across datasets, performing as well or better than resting-state or task data alone. Collectively, our work suggests that GFC can improve the reliability of intrinsic connectivity estimates in existing datasets and, subsequently, the opportunity to identify meaningful correlates of individual differences in behavior. Given that task and resting-state data are often collected together, many researchers can immediately derive more reliable measures of intrinsic connectivity through the adoption of GFC rather than solely using resting-state data. Moreover, by better capturing heritable variation in intrinsic connectivity, GFC represents a novel endophenotype with broad applications in clinical neuroscience and biomarker discovery.