Model systems (of up to 116 atoms) for molecular crystals and mismatched pairs of DNA bases have been studied using GGA density functional theory (DFT) at BP86/TZ2P. In line with previous studies, we find that our approach is adequate for accurately describing the present model systems all of which involve hydrogen bonding. For example, our DFT bond energies for 17 DNA base pairs involving adenine (A), thymine (T), guanine (G), and cytosine (C) agree excellently with ab initio MP2 results (root-mean-square deviation = 1.1 kcal/mol). Our main purpose is to clarify the relative importance of electrostatic attraction versus orbital interaction in the hydrogen bonds involved in our model systems, using a quantitative bond energy decomposition scheme. At variance with widespread belief, the orbital interaction component in these hydrogen bonds is found to contribute about two-fifths (36-43%) of the attractive interactions and is thus of the same order of magnitude as the electrostatic component. Interestingly, we find a similarly prominent role for orbital interaction in the hydrogen bonds that are responsible for the cohesion within a layer of the molecular crystal of Watson-Crick pairs of 9-ethylguanine and 1-methylcytosine.