We present a molecular-dynamics study of the self-dynamics of water molecules in deeply supercooled liquid states. We find that the decay of single-particle dynamics correlation functions is characterized by a fast initial relaxation toward a plateau and by a region of self-similar dynamics, followed at late times by a stretched exponential decay. We interpret such results in the framework of the mode-coupling theory for supercooled liquids. We relate the apparent anomalies of the transport coefficients in water on lowering the temperature to the formation of cages and to the associated slow dynamics resulting from the presence of long-lived molecular cages. The so-called critical Angell temperature in supercooled water could thus be interpreted as kinetic glass transition temperature, relaxing the need of a thermodynamic singularity for the explanation of the anomalies of Liquid water.