We think of DNA as double-stranded helices (duplex), but the polymer exists in many conformations. Several triplex and quadruplex DNA structures can be formed in laboratory settings and exist in nature. This thesis first provides a brief description of the nature of the order in arrays of duplex DNA under biologically relevant molecular crowding conditions. Then we compare the duplex DNA mesophases with the corresponding liquid crystalline phase behavior of the triplex and quadruplex DNA analogues. In particular, we focus on G-quadruplexes. Observed in the folds of guanine-rich oligonucleotides, G-quadruplex structures are based on G-quartets formed by hydrogen bonding and cation-coordination of guanosines. In dilute 5'-guanosine monophosphate (GMP) solutions, G-quartets form by the self-assembly of four GMP nucleotides. We use x-ray diffraction to characterize the columnar liquid-crystalline mesophases in concentrated solutions of various model G-quadruplexes. We then probe the transitions between mesophases by varying the PEG solution osmotic pressure, thus mimicking in vivo molecular crowding conditions. Using the GMP-quadruplex, built by the stacking of G-quartets with no covalent linking between them, as the baseline, we report the liquid-crystalline phase behaviors of two other related G-quadruplexes: (i) the intramolecular parallel-stranded G-quadruplex formed by the 22-mer four-repeat human telomeric sequence AG3(TTAG3)3 and (ii) the intermolecular parallel-stranded G-quadruplex formed by the TG4T oligonucleotides. Finally, we compare the mesophases of the G-quadruplexes, under PEG-induced crowding conditions, with the corresponding mesophases of the canonical duplex and triplex DNA analogues. The mesophase transitions of higher-order DNA structures, i.e., triplexes and quadruplexes, have nature and features similar to the cholesteric-hexatic transition of duplex DNA. We explore the sensitivity of the DNA mesophase transitions (including the DNA density change at the transition) to thermodynamic variables such as osmotic pressure, ionic strength, and temperature. Measurements of the mesophase transitions of DNA analogues reveal relations between high-density DNA packing and the helical and elastic characteristics of the DNA structures.