Up till now, there has been a significant disagreement between theory and experiment regarding hydrogen bond lengths in Watson-Crick base pairs. To investigate the possible sources of this discrepancy, we have studied numerous model systems for adenine-thymine (AT) and guanine-cytosine (GC) base pairs at various levels (i.e., BP86, PW91, and BLYP) of nonlocal density functional theory (DFT) in combination with different Slater-type orbital (STO) basis sets. Best agreement with available gas-phase experimental A-T and G-C bond enthalpies (-12.1 and -21.0 kcal/mol) is obtained at the BP86/TZ2P level, which (for 298 K) yields -11.8 and -23.8 kcal/mol. However, the computed hydrogen bond lengths show again the notorious discrepancy with experimental values. The origin of this discrepancy is not the use of the plain nucleic bases as models for nucleotides: the disagreement with experiment remains no matter if we use hydrogen, methyl, deoxyribose, or 5'-deoxyribose monophosphate as the substituents at N9 and N1 of the purine and pyrimidine bases, respectively. Even the BP86/DZP geometry of the Watson-Crick-type dimer of deoxyadenylyl-3',5'-deoxyuridine including one Na+ ion (with 123 atoms our largest model for sodium adenylyl-3',5'-uridine hexahydrate, the crystal of which had been studied experimentally with the use of X-ray diffraction) still shows this disagreement with experiment. The source of the divergence turns out to be the molecular environment (water, sugar hydroxyl groups, counterions) of the base pairs in the crystals studied experimentally. This has been missing, so far, in all theoretical models. After we had incorporated the major elements of this environment in our model systems, excellent agreement between our BP86/TZ2P geometries and the X-ray crystal structures was achieved.