We analyze the relevance of finite-size effects to the electronic structure of long graphene nanoribbons using a divide and conquer density functional approach. We find that for hydrogen terminated graphene nanoribbons, most of the physical features appearing in the density of states of an infinite graphene nanoribbon are recovered at a length of 40 nm. Nevertheless, even for the longest systems considered (72 nm long) pronounced edge effects appear in the vicinity of the Fermi energy. The weight of these edge states scales inversely with the length of the ribbon, and they are expected to become negligible only at ribbons lengths of the order of micrometers. Our results indicate that careful consideration of finite-size and edge effects should be applied when designing new nanoelectronic devices based on graphene nanoribbons. These conclusions are expected to hold for other one-dimensional systems such as carbon nanotubes, conducting polymers, and DNA molecules.