Recent work has made important advances in describing the large-scale systems-level organization of human cortex by analyzing functional magnetic resonance imaging (fMRI) data averaged across groups of subjects. However, new findings have emerged suggesting that individuals' cortical systems are topologically complex, containing small but reliable features that cannot be observed in group-averaged datasets, due in part to variability in the position of such features along the cortical sheet. This previous work has reported only specific examples of these individual-specific system features; to date, such features have not been comprehensively described. Here we used fMRI to identify cortical system features in individual subjects within three large cross-subject datasets and one highly sampled within-subject dataset. We observed system features that have not been previously characterized, but 1) were reliably detected across many scanning sessions within a single individual, and 2) could be matched across many individuals. In total, we identified forty-three system features that did not match group-average systems, but that replicated across three independent datasets. We described the size and spatial distribution of each non-group feature. We further observed that some individuals were missing specific system features, suggesting individual differences in the system membership of cortical regions. Finally, we found that individual-specific system features could be used to increase subject-to-subject similarity. Together, this work identifies individual-specific features of human brain systems, thus providing a catalog of previously unobserved brain system features and laying the foundation for detailed examinations of brain connectivity in individuals.