We analyze the coupling between surface plasmon polaritons in a metal grating and the guided modes of a dielectric waveguide. Our model structure is a gold wire grating on a slab waveguide made of silicon nitride on silica wafer. The excitation of guided-mode resonances, surface plasmon polariton modes and hybrid waveguide-plasmon modes are observed in numerical simulations. Our experiments verify the existence of the predicted modes. These hybrid modes add significant degrees of freedom in designing structures for plasmonic applications.