We compare dielectric relaxation tau(T) data of several low molecular weight glass-forming liquids with the predictions of the Adam-Gibbs theory using experimental data for the configurational entropy S-c(T). Combination of Adam-Gibbs and Vogel-Fulcher equations yields an expression for S-c(T) which can be compared with experimental data. Good agreement is found for a range of temperatures near T-g < T< T-B which depends on the fragility of the liquid and on the presence of a beta relaxation. For fragile liquids, T-B coincides with a qualitative change in the temperature dependence of the relaxation time scale or viscosity, with the temperature T-beta, where Johari-Goldstein-type beta processes tend to merge into the alpha process, and with other crossover temperatures. For nonfragile liquids, T-B/T-g increases, and the deviations from the Adam-Gibbs equation weaken or disappear altogether. The significance of T-B, and of the S-c(T) temperature dependence implied by the Vogel-Fulcher theory fitting, are discussed in terms of the landscape paradigm.