Dynamic localization is the suppression of the broadening of a charged-particle wave packet as it moves along a periodic potential in an a.c. electric field1-3. The same effect occurs for optical beams in curved photonic lattices, where the lattice bending has the role of the driving field, and leads to the cancellation of diffraction4-8. Dynamic localization was also observed for Bose-Einstein condensates9, and could have a role in the spin dynamics of molecular magnets10. It has been predicated that dynamic localization will occur in multidimensional lattices at a series of resonances between lattice, particle and driving-field parameters1. However, only the first dynamic localization resonance in one-dimensional lattices has been observed in any physical system 6-9. Here, we report on the experimental observation of higher-order and mixed dynamic localization resonances in both one- and two-dimensional photonic lattices. New features such as spectral broadening of the dynamic localization resonances and localization-induced transformation of the lattice symmetry are demonstrated. These phenomena could be used to shape polychromatic beams emitted by supercontinuum light sources11,12.