The electronic structure of substituted molecules is governed, to a significant extent, by the substituent effect (SE). In this paper, SEs in selected nucleic acid base pairs (Watson-Crick, Hoogsteen, adenine-adenine) are analyzed, with special emphasis on their influence on intramolecular interactions, aromaticity, and base pair hydrogen bonding. Quantum chemistry methods—DFT calculations, the natural bond orbital (NBO) approach, the Harmonic Oscillator Model of Aromaticity (HOMA) index, the charge of the substituent active region (cSAR) model, and the quantum theory of atoms in molecules (QTAIM)—are used to compare SEs acting on adenine moiety and H-bonds from various substitution positions. Comparisons of classical SEs in adenine with those observed in para- and meta-substituted benzenes allow for the better interpretation of the obtained results. Hydrogen bond stability and its other characteristics (e.g., covalency) can be significantly changed as a result of the SE, and its consequences are dependent on the substitution position. These changes allow us to investigate specific relations between H-bond parameters, leading to conclusions concerning the nature of hydrogen bonding in adenine dimers—e.g., H-bonds formed by five-membered ring nitrogen acceptor atoms have an inferior, less pronounced covalent nature as compared to those formed by six-membered ring nitrogen. The energies of individual H-bonds (obtained by the NBO method) are analyzed and compared to those predicted by the Espinosa-Molins-Lecomte (EML) model. Moreover, both SE and H-bonds can significantly affect the aromaticity of adenine rings; long-distance SEs on π-electron delocalization are also documented.