Nucleosides are chemical compounds that have an extremely important biological role; they can be found in all types of living organisms. They are crucial components from which DNA and RNA acids are built. In addition, nucleosides are key regulators of many physiological processes. In this paper, the molecular dynamics in the liquid and glassy state of three selected nucleosides, β-adenosine, β-thymidine, and β-uridine, was investigated by means of dielectric spectroscopy. Our results revealed multiple relaxation processes associated with different types of molecular motions. Besides the primary α relaxation, two secondary modes in the glassy states of examined compounds were identified. Crystallization progress monitored by dielectric spectroscopy and x-ray diffraction technique at isostructural relaxation conditions revealed that the examined nucleosides possess completely different tendencies to recrystallize from the liquid as well as the glassy state. We have also made an attempt to predict the time scale of molecular motion below the glass transition temperatures of the respective nucleosides to discuss their potential stability at room temperature over prolonged storage time. Finally, combination of molecular mobility studies with evaluation of thermodynamic parameters from calorimetric measurements allowed us to discuss the fundamental roles of both kinetic and thermodynamic factors in governing the physical stability of the glassy state.