Graphane is a two-dimensional system consisting of a single planar layer of fully saturated carbon atoms, which has recently been realized experimentally through hydrogenation of graphene membranes. We have studied the stability of chair, boat, and twist-boat graphane structures using first-principles density functional calculations. Our results indicate that locally stable twist-boat membranes significantly contribute to the experimentally observed lattice contraction. The band gaps of graphane nanoribbons decrease monotonically with the increase of the ribbon width and are insensitive to the edge structure. The implications of these results for future hydrogenated graphene applications are discussed.