We report evidence for extended gamma-ray emission from the Virgo, Fornax and Coma clusters based on a maximum-likelihood analysis of the 3-year Fermi-LAT data. For all three clusters, excess emission is observed within three degrees of the center, peaking at the GeV scale. This emission cannot be accounted for by known Fermi sources or by the galactic and extragalactic backgrounds. If interpreted as annihilation emission from supersymmetric dark matter (DM) particles, the data prefer models with a particle mass in the range 20-60 GeV annihilating into the b-bbar channel, or 2-10 GeV and >1 TeV annihilating into mu-mu final states. Our results are consistent with those obtained by Hooper and Linden from a recent analysis of Fermi-LAT data in the region of the Galactic Centre. An extended DM annihilation profile dominated by emission from substructures is preferred over a simple point source model. The significance of DM detection is 4.4 sigma in Virgo and lower in the other two clusters. We also consider the possibility that the excess emission arises from cosmic ray (CR) induced gamma-rays, and infer a CR level within a factor of three of that expected from analytical models. However, the significance of a CR component is lower than the significance of a DM component, and there is no need for such a CR component in the presence of a DM component in the preferred DM mass range. We also set flux and cross-section upper limits for DM annihilation into the b-bbar and mu-mu channels in all three clusters.