Time-dependent density functional theory (TDDFT) is a powerful tool allowing for accurate description of excited states in many nanoscale molecular systems; however, its application to large molecules may be plagued with difficulties that are not immediately obvious from previous experiences of applying TDDFT to small molecules. In TDDFT, the appearance of spurious charge-transfer states below the first optical excited state is shown to have significant effects on the predicted absorption and emission spectra of several donor-acceptor substituted molecules. The same problem affects the predictions of electronic spectra of molecular aggregates formed from weakly interacting chromophores. For selected benchmark cases, we show that today's popular density functionals, such as purely local (Local Density Approximation, LDA) and semilocal (Generalized Gradient Approximation, GGA) models, are qualitatively wrong. Nonlocal hybrid approximations including both semiempirical (B3LYP) and ab initio (PBE1PBE) containing a small fraction (20-25%) of Fock-like orbital exchange are also susceptible to such problems. Functionals that contain a larger fraction (50%) of orbital exchange like the early hybrid (BHandHLYP) are shown to exhibit far fewer spurious charge-transfer (CT) states at the expense of accuracy. Based on the trends observed in this study and our previous experience we formulate several practical approaches to overcome these difficulties providing a reliable description of electronic excitations in nanosystems.