Increased interest in molecular time scares below the glass transition temperature, T-g, has arisen from the desire to identify the conditions (e.g., temperature) where the molecular processes which lead to unwanted changes in amorphous systems (e.g., chemical reactivity, crystallization, structural collapse) are improbable. The purpose of this study was to characterize the molecular mobility of selected amorphous systems (i.e., indomethacin, sorbitol, sucrose, and trehalose) below T-g using a combined experimental and theoretical approach. Of particular interest was the temperature where the time scales for molecular motion (i.e., relaxation time) exceed expected lifetimes or storage times. As a first approximation of this temperature, the temperature where the thermodynamic properties of the crystal and the equilibrium supercooled liquid converge (i.e., the Kauzmann temperature, T-K) was determined. T-K values derived from heat capacity and enthalpy of fusion data ranged from 40 to 190 K below the calorimetric T-g. A more refined approach, using a form of the Vogel-Tamman-Fulcher (VTF) equation derived from the Adam-Gibbs formulation for nonequilibrium systems below T-g, was used to predict the temperatures where the relaxation times of real glasses exceed practical storage times. Relaxation times in glasses were characterized in terms of their fictive temperature, as determined from heat capacity data measured using modulated differential scanning calorimetry. The calculated relaxation times were in good agreement with measured relaxation times for at least two materials. Relaxation times in real glasses were on the order of three years at temperatures near T-K, indicating low (but not zero) mobility under conditions where the equilibrium supercooled liquid experiences total loss of structural mobility. The results of this study demonstrate the importance of excess configurational entropy formed during vitrification in determining structural relaxation dynamics in real glasses.