Monte Carlo computer simulations were performed on dilute aqueous solutions of thymine, cytosine, uracil, adenine, guanine, the dimethyl phosphate anion in the gauche-gauche conformation and a ribose and deoxyribose derivative. The aqueous hydration of each molecule was analysed in terms of quasi-component distribution functions based on the Proximity Criterion, and partitioned into hydrophobic, hydrophilic and ionic contributions. Color stereo views of selected hydration complexes are also presented. A preliminary discussion of the transferability of functional group coordination numbers is given. The results enable to comment on two current problems related to the hydration of nucleic acids: a) the theory of Dickerson and coworkers on the role of water in the relative stability of the A and B form of DNA and b) the idea of water bridges and filaments emerging from the computer simulation results on the hydration of DNA fragments by Clementi.