The character of the ground state of an antiferromagnetic insulator is fundamentally altered following addition of even a small amount of charge(1). The added charge is concentrated into domain walls across which a pi phase shift in the spin correlations of the host material is induced. In two dimensions, these domain walls are ＇stripes＇ which can be insulating(2,3) or conducting(4-6)-that is, metallic ＇rivers＇ with their own low-energy degrees of freedom. However, in arrays of one-dimensional metals, which occur in materials such as organic conductors(7), interactions between stripes typically drive a transition to an insulating ordered charge-density-wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large compared to the CDW coupling between stripes. As a consequence, there should exist electronic quantum liquid-crystal phases, which constitute new states of matter, and which can be either high-temperature superconductors or two-dimensional anisotropic ＇metallic＇ non-Fermi liquids. Neutron scattering and other experiments in the copper oxide superconductor La1.6-xNd0.4SrxCuO4 already provide evidence for the existence of these phases in at least one class of materials.