We study the length dependence of electron transport through three families of rigid, ribbonlike molecular wires. These series of molecules, known as polyacene dithiolates, polyphenanthrene dithiolates, and polyfluorene dithiolates, represent the ultimate graphene nanoribbons. We find that acenes are the most attractive candidates for low-resistance molecular-scale wires because the low-bias conductance of the fluorene- and phenanthrene-based families is shown to decrease exponentially with length, with inverse decay lengths of beta = 0.29 angstrom(-1) and beta = 0.37 angstrom(-1), respectively. In contrast, the conductance of the acene-based series is found to oscillate with length due to quantum interference. The period of oscillation is determined by the Fermi wave vector of an infinite acene chain and is approximately 10 angstrom. Details of the oscillations are sensitive to the position of thiol end groups and in the case of "para" end groups, the conductance is found initially to increase with length.