The effect of chemical structure on the segmental relaxation behavior is examined for a wide range of polymers. Both the time and temperature dependence of the glass transition dispersion in the dielectric loss spectrum are shown to be correlated with the degree to which local structure engenders steric constraints on the relaxation from neighboring nonbonded segments. The polymers studied exhibit a range of segmental relaxation behavior. For polymers with smooth, compact, symmetrical chain backbones, segmental relaxation times have a near Arrhenius temperature dependence, representing the limiting-type behavior associated with relatively unconstrained (“Debye”) relaxation. Polymers having less flexible backbones and/or sterically-hindering pendant groups exhibit broad segmental dispersions and temperature dependencies near the extreme fragile edge; these characteristics reflect segmental relaxation that is strongly intermolecularly cooperative. The data for polymers parallel observations made on small-molecule glass-forming liquids, whose chemical structure similarly governs the strength of the intermolecular coupling, and thus the time and temperature dependence of segmental relaxation.