NMR spectroscopy (H-2 and H-1), polarized-light optical microscopy, and synchrotron X-ray diffraction have been used to determine the liquid-crystal structures (mesophases) formed at room temperature by four anionic cyanine dyes in water. A sharp, intense, bathochromically-shifted absorption band appeared in the UV-visible absorption spectra on increasing dye concentration for all the dyes, demonstrating that so-called J-aggregates are formed. The onset of J-aggregate formation is practically concomitant with the occurrence of mesophases. In some instances, these mesophases form. at much less than 0.1% w/w. X-ray diffraction shows that three of the dyes form layer (lamellar) phases while one forms columnar nematic and hexagonal phases, These structures are consistent with the textures observed by optical microscopy. Unusually, the columns have a multimolecular cross section rather than being unimolecular. We propose a novel "hollow pipe" structure for these aggregates. The liquid-crystal type appears to be largely dependent on the precise molecular structure of the dye, presumably due to the short-range intermolecular interactions (electrostatic, steric, and van der Waals). Previously postulated stacking geometries for low-dimensional J-aggregates are compared to the liquid-crystal structures. Since the J-aggregates form a separate liquid-crystalline phase they consist of thousands of molecules or more, rather than the small aggregation numbers deduced by mass action considerations.