Because of their unique photophysical properties, organic semiconductors have shown great promise in both light-emitting devices (LEDs) and photovoltaic systems. In particular, the question of spin statistics looms large in these applications: the relative energetics and rates of formation for singlet versus triplet excited states can have a significant impact on device efficiency. In this Article, we study the singlet and triplet charge-transfer (CT) configurations that can be thought of as the immediate precursors to the luminescent states in organic LEDs. In particular, we find that the CT singlet-triplet energy gap (Delta E-ST) of organic dyes and oligomers depends sensitively on both the material and the relative orientation of the donor/acceptor pair. Furthermore, in contrast with the commonly held view, we find that the singlet CT states nearly always lie energetically below the triplet CT states (Delta E-ST < 0). This trend is attributed to two physical sources. First, the relatively close contact between the donor and acceptor leads to a strong kinetic exchange component that favors the singlet. Second, Coulombic attraction between the separated charges favors inner-sphere reorganization that brings the donor and acceptor closer together, further enhancing the kinetic exchange effect. We discuss the implications of these results on the design of organic LEDs.