We observe the appearance of Fano resonances in the optical response of plasmonic nanocavities due to the coherent coupling between their superradiant and subradiant plasmon modes. Two reduced-symmetry nanostructures probed via confocal spectroscopy, a dolmen-style slab arrangement and a ring/disk dimer, clearly exhibit the strong polarization and geometry dependence expected for this behavior at the individual nanostructure level, confirmed by full-field electrodynamic analysis of each structure. In each case, multiple Fano resonances occur as structure size is increased.