We have analyzed and compared the available experimental data (PDB) on the backbone geometry of the DNA in solution (NMR), in crystals (X-rays), and in complexes with proteins (X-rays and cryo-electron microscopy). The deoxyribose (pseudorotational angle tau(0)) and epsilon/zeta (BI-BII transition in phosphates) flexibilities are practically the same in the four samples. The alpha/gamma mobility is minimal in crystalline DNA: on the histograms, there is one canonical and one noncanonical t/t peak. The alpha/gamma mobility increases in DNA solutions (three more noncanonical peaks) and is maximal in DNA-protein complexes (another additional peak). On a large amount of data, we have confirmed that the three main degrees of freedom of the sugar-phosphate backbone are "orthogonal": changes in any of the angles tau(0), (zeta-epsilon), and (gamma-alpha) occur, as a rule, at a constant (usually canonical) value of any other. In the DNA-protein complexes, none of the geometrical parameters commonly used to distinguish the A and B forms of DNA, except for Zp and its simpler analog Zp', show an unambiguous correlation with tau(0). Proteins, binding to DNA, in 59% of cases change the local shape of the helix up to the characteristic of the A-form without switching the deoxyribose conformation from south to north. However, we have found simple local characteristics of one nucleotide that correlate with the angles tau(0) and (zeta-epsilon). These are the angles C3'Cl'N* and C4'C3'P(2), respectively. They are orthogonal in DNA-protein complexes exactly as the pair tau(0) and (zeta-epsilon). Most characteristics of DNA in complexes with proteins are the same in X-ray and in cryo-EM data, except for the histogram for the angle tau(0). We offer a possible explanation for this difference. We also discuss the artifacts on the epsilon/zeta histogram for DNA in solutions caused by the currently used NMR refinement protocols.