An increasing number of functional magnetic resonance imaging (fMRI) studies have revealed potential neural substrates of individual differences in diverse types of brain function and dysfunction. Although most previous studies have inherently focused on state-specific characterizations of brain networks and their functions, several recent studies reported on the potential state-unspecific nature of functional brain networks, such as global similarities across different experimental conditions or states, including both task and resting states. However, no previous studies have carried out direct, systematic characterizations of state-unspecific brain networks, or their functional implications. Here, we quantitatively identified several modes of state-unspecific individual variations in whole-brain functional connectivity patterns, called "Common Neural Modes" (CNMs), from a large-scale fMRI database including eight task/resting states. Furthermore, we tested how CNMs accounted for variability in individual cognitive measures. The results revealed that three CNMs were robustly extracted under various dimensions of features used. Each of these CNMs was preferentially correlated with different aspects of representative cognitive measures, reflecting stable individual traits. Importantly, the association between CNMs and cognitive measures emerged from brain connectivity data alone ("unsupervised"), whereas previous related studies have explicitly used both connectivity and cognitive measures to build their prediction models ("supervised"). The three CNMs were also able to predict several life outcomes, including income and life satisfaction, and achieved the highest level of performance when combined with a conventional cognitive measure. Our findings highlight the importance of state-unspecific brain networks in characterizing fundamental individual variation.