The large majority of extragalactic star cluster studies performed to date essentially use multi-colour photometry, combined with theoretical stellar synthesis models, to derive ages, masses, extinction estimates, and metallicities. M31 offers a unique laboratory for studies of globular cluster (GC) systems. In this paper, we obtain new age estimates for 91 M31 globular clusters, based on improved photometric data, updated theoretical stellar synthesis models and sophisticated new fitting methods. In particular, we used photometric measurements from the Two Micron All Sky Survey (2MASS), which, in combination with optical photometry, can partially break the well-known age-metallicity degeneracy operating at ages in excess of a few Gyr. We show robustly that previous age determinations based on photometric data were affected significantly by this age-metallicity degeneracy. Except for one cluster, the ages of our other sample GCs are all older than 1 Gyr. Their age distribution shows populations of young and intermediate-age GCs, peaking at $\sim3$ and 8 Gyr respectively, as well as the usual complement of well-known old GCs, i.e., GCs of similar age as the majority of the Galactic GCs. Our results also show that although there is significant scatter in metallicity at any age, there is a noticeable lack of young metal-poor and old metal-rich GCs, which might be indicative of an underlying age-metallicity relationship among the M31 GC population.