The terahertz absorption coefficient, index of refraction, and conductivity of nanostructured ZnO have been determined using time-resolved terahertz spectroscopy, a noncontact optical probe. ZnO properties were measured directly for thin films and were extracted from measurements of nanowire arrays and mesoporous nanoparticle films by applying Bruggeman effective medium theory to the composite samples. Annealing significantly reduces the intrinsic carrier concentration in the ZnO films and nanowires, which were grown by chemical bath deposition. The complex-valued, frequency-dependent photoconductivities for all morphologies were found to be similar at short pump-probe delay times. Fits using the Drude-Smith model show that films have the highest mobility, followed by nanowires and then nanoparticles, and that annealing the ZnO increases its mobility. Time constants for decay of photoinjected electron density in films are twice as long as those in nanowires and more than 5 times those for nanoparticles due to increased electron interaction with interfaces and grain boundaries in the smaller-grained materials. Implications for electron transport in dye-sensitized solar cells are discussed.