Steady states of driven lattice gases with open boundaries are investigated. Particles are fed into the system at one edge, travel under the action of an external field, and leave the system at the opposite edge. Two types of phase transitions involving nonanalytic changes in the density profiles and the particle number fluctuation spectra are encountered upon varying the feeding rate and the particle interactions, and associated diverging length scales are identified. The principle governing the transitions is the tendency of the system to maximize the transported current. © 1991 The American Physical Society.