We study the chemical abundances of a wide sample of 142 Galactic planetary nebulae (PNe) with good-quality observations, for which the abundances have been derived more or less homogeneously, thus allowing a reasonable comparison with stellar models. The goal is the determination of mass, chemical composition and formation epoch of their progenitors through comparison of the data with results from asymptotic giant branch (AGB) evolution. The dust properties of PNe, when available, were also used to further support our interpretation. We find that the majority (˜60 per cent) of the Galactic PN studies have nearly solar chemical composition, while ˜40 per cent of the sources investigated have subsolar metallicities. About half of the PNe have carbon star progenitors, in the 1.5 M⊙ < M < 3 M⊙ mass range, which have formed between 300 Myr and 2 Gyr ago. The remaining PNe are almost equally distributed among PNe enriched in nitrogen, which we interpret as the progeny of M > 3.5 M⊙ stars, younger than 250 Myr, and a group of oxygen-rich PNe, descending from old (>2 Gyr) low-mass (M < 1.5 M⊙) stars that never became C-stars. This analysis confirms the existence of an upper limit to the amount of carbon that can be accumulated at the surface of carbon stars, probably due to the acceleration of mass-loss in the late AGB phases. The chemical composition of the present sample suggests that in massive AGB stars of solar (or slightly subsolar) metallicity, the effects of third dredge-up combine with hot bottom burning, resulting in nitrogen-rich - but not severely carbon depleted - gaseous material to be ejected.