The conductivity of DNA covalently bonded to a gold surface was studied by means of the STM technique. Various single- and double-stranded 32-nucleotide-long DNA sequences were measured under ambient conditions so as to provide a better understanding of the complex process of charge-carrier transport in natural as well as chemically modified DNA molecules. The investigations focused on the role of several features of DNA structure, namely the role of the negative charge at the backbone phosphate group and the related complex effects of counterions, and of the stacking interactions between the bases in Watson-Crick and other types of base pairs. The measurements have indicated that the best conductor is DNA in its biologically most relevant double-stranded form with Watson-Crick base pairs and charged phosphates equilibrated with counterions and water. All the studied modifications, including DNA with non-Watson-Crick base pairs, the abasic form, and especially the form with phosphate charges eliminated by chemical modifications, lower the conductivity of natural DNA.