Ab initio coupled (random phase approximation) and uncoupled (sum over states) Hartree-Fock calculations of the asymptotic longitudinal polarizabilities are carried out for conjugated infinite periodic systems with a carbon backbone: polyacetylene, polyyne, polydiacetylene, and polybutatriene. Direct polymeric methods are employed and compared to values extrapolated from finite oligomeric longitudinal polarizability calculations and to available experimental values. For polybutatriene where finite oligomeric calculations failed to give the asymptotic value, we estimate the asymptotic longitudinal polarizabilities per unit length to be 19.3 and 68.4 atomic units in the minimal STO-3G atomic basis at the uncoupled and coupled Hartree-Fock levels, respectively.