Based on a new large, homogeneous photometric database of 34 Galactic globular clusters (GGCs plus Palomar 12), a set of distance- and reddening- independent relative age indicators has been measured. The observed δ(V-I)2.5 and ΔVHBTO versus metallicity relations have been compared with the relations predicted by two recently updated libraries of isochrones. Using these models and two independent methods, we have found that self-consistent relative ages can be estimated for our GGC sample. In turn, this demonstrates that the models are internally self-consistent. Based on the relative age versus metallicity distribution, we conclude that (1) there is no evidence of an age spread for clusters with [Fe/H]<-1.2, all the clusters of our sample in this range being old and coeval; (2) for the intermediate-metallicity group (-1.2<=[Fe/H]<-0.9), there is a clear evidence of age dispersion, with clusters up to ~25% younger than the older members; and (3) the clusters within the metal-rich group ([Fe/H]>=-0.9) seem to be coeval within the uncertainties (except Pal 12) but younger (~17%) than the bulk of the GGCs. The latter result is totally model dependent. From the Galactocentric distribution of the GGC ages, we can divide the GGCs in two groups: the old, coeval clusters and the young clusters. The second group can be divided into two subgroups: the ``really young clusters'' and the ``young, but model dependent,'' which are within the intermediate- and high-metallicity groups, respectively. From this distribution, we can present a possible scenario for the Milky Way's formation: The globular cluster formation process started at the same zero age throughout the halo, at least out to ~20 kpc from the Galactic center. According to the present stellar evolution models, the metal-rich clusters are formed at a later time (~17% lower age). Finally, significantly younger halo GGCs are found at any RGC>8 kpc. For these, a possible scenario associated with mergers of dwarf galaxies to the Milky Way is suggested.