The quantum transport properties of graphene nanoribbon networks are investigated using first-principles calculations based on density functional theory. Focusing on systems that can be experimentally realized with existing techniques, both in-plane conductance in interconnected graphene nanoribbons and tunneling conductance in out-of-plane nanoribbon intersections were studied. The characteristics of the ab initio electronic transport through in-plane nanoribbon cross-points is found to be in agreement with results obtained with semiempirical approaches. Both simulations confirm the possibility of designing graphene nanoribbon-based networks capable of guiding electrons along desired and predetermined paths. In addition, some of these intersections exhibit different transmission probability for spin up and spin down electrons, suggesting the possible applications of such networks as spin filters. Furthermore, the electron transport properties of out-of-plane nanoribbon cross-points of realistic sizes are described using a combination of first-principles and tight-binding approaches. The stacking angle between individual sheets is found to play a central role in dictating the electronic transmission probability within the networks.