We report a detailed optical study of several sets of multiple quantum wells (MQWs) in the AlGaN/GaN system, as well as AlN/GaN superlattice (SL) structures. In this study all materials were grown by MOCVD, as opposed to most previous studies where MBE was employed. In undoped MQWs discrete photoluminescence (PL) peaks related to discrete well width fluctuations by one full c lattice parameter are clearly observed. In doped samples this effect appears to be screened. While the recombination process in undoped samples is excitonic, in MQWs doped with Si above about 5 x 10(18) cm(-3) free electrons (a 2DEG) are dominant, and the PL process is a free electrons-localized hole transition at low temperatures. The hole localization prevails up to very high n-doping, as was previously observed in bulk GaN. The hole localization is demonstrated via several experiments, including results on PL transient decay times and LO phonon coupling. Near surface band bending, due mainly to dopant depletion in doped structures or interaction with surface states in case of higher Al content in barriers, influences the distribution of electron filling among the QWs, making a detailed modeling of the spectral shape somewhat ambiguous. It is found that AlN barriers promote a strong room temperature PL signal from the QWs, as opposed to the case with AlGaN barriers.