Strong plasmonic-molecular resonance coupling occurs between noble metal nanocrystals and organic adsorbates when the plasmonic resonance is degenerate with the molecular one. This interaction forms the basis for many fundamental studies and practical applications. We describe here the first direct measurement of the resonance coupling on single gold nanorods. The dark-field scattering technique is employed. The nanorods are embedded in hydrogel to facilitate uniform dye adsorption. The adsorbed dye molecules exhibit both monomer and H-aggregate absorption bands. The same gold nanorods are measured before and after the dye adsorption. Both strong and weak coupling are investigated by selecting nanorods with different longitudinal plasmon bands. Excellent agreement between the experiments and an analytic theory is obtained. The resonance coupling reveals a unique three-band structure. The tunability of the coupling on individual nanorods is further demonstrated by photodecomposing the adsorbed dye molecules.