Noncanonical parallel-stranded DNA double helices (ps-DNA) comprising natural nucleotide sequences are usually second in stability to antiparallel-stranded (aps) canonical DNA structures, which ensures reliable cell functioning. However, recent data indicate a possible role of ps-DNA in DNA loops or in trinucleotide repeats connected with neurodegenerative diseases. The review surveys recent studies on the effect of nucleotide sequence on preference of one or other type of DNA duplex. (1) Ps-DNA with mixed AT/GC composition was found to have conformational and thermodynamic properties drastically different from those of Watson-Crick double helix. Its stability depends strongly on the specific sequence in a manner peculiar to the ps double helix, because of the energy disadvantage of the AT/GC contacts. The AT/GC boundary facilitated flipping of A and T out of the ps double helix. Proton acceptor groups of bases are exposed into the both grooves of the ps-DNA and are accessible to solvent and ligands, including proteins. (2) DNA regions containing natural minor bases isoguanine and isomethylcytosine were shown to form ps-DNA with transAT-, trans isoGC, and trans iso5meCG pairs exceeding in stability a related aps duplex. (3) Nucleotide sequence dG(GT)4G from yeast telomeres and microsatellites was demonstrated to form novel ps-DNA with GG and TT base pairing. Unlike d(GT)n and d(GnTm) sequences able to form quadruplexes, the dG(GT)4G sequence formed no alternative double- or multistranded structures in a wide range of experimental conditions, thus suggesting that the nucleotide context governs the observed structural polymorphism of the d(GT)n sequence. The possible biological role of ps-DNA and the prospects of its study are discussed.