Density functional calculations have been performed for many isomers of neutral carbon clusters C-n (4 less than or equal to n less than or equal to 32, n even) using both local spin density (LSD) and gradient-corrected (Becke-Perdew) approximations to the exchange-correlation energy. The stable isomers include chains, rings, cages, and graphitic ("plate＇＇ and "bowl＇＇) structures, and we observe a fourfold periodicity in several structural classes as n changes. Stable cages exist for all clusters with n greater than or equal to 8, and double rings are less stable than the monocyclic rings in all cases. Most planar structures have low-frequency out-of-plane vibrations. Gradient corrections often change the ordering of the energies of the isomers, but the effects are remarkably regular within a given structural type.