Vertical electronic excitations in model systems representing single-and double-stranded B-DNA are characterized using electronic structure theory, including both time-dependent density functional theory (TD-DFT) and correlated wave function techniques. Previous TD-DFT predictions of charge-transfer (CT) states well below the optically bright (1)pi pi* states are shown to be artifacts of the improper long-range behavior of standard density-functional exchange approximations, which we rectify here using a long-range correction (LRC) procedure. For nucleobase dimers (hydrogen-bonded or pi-stacked), TD-LRC-DFT affords vertical excitation energies in reasonable agreement with the wave function methods, not only for the (1)n pi* and (1)pi pi* states but also for the CT states, and qualitatively reproduces well-known base-stacking effects on the absorption spectrum of DNA. The emergence of (1)pi pi* Frenkel exciton states, localized on a single strand, is clearly evident, and these states (rather than low-energy CT states) are primarily responsible for the fact that DNA's absorption spectrum exhibits a red tail that is absent in monomer absorption spectra. For B-DNA in aqueous solution, the low-energy tail of the CT band (representing both intra- and interstrand CT states) appears at energies comparable to those of the optically bright (1)pi pi* exciton states. In systems with more than one base pair, we also observe the emergence of delocalized, interstrand CT excitations, whose excitation energies may be significantly lower than the lowest CT excitation in a single base pair. Together, these observations suggest that a single Watson-Crick base pair is an inadequate model of the photophysics of B-DNA.