High sensitivity of surface-plasmon-based sensors stems from the fact that the surface plasmon is a resonance phenomenon. The resonance results from the phase-matching condition when the phase velocity of the surface plasmon wave and of the lateral component of the incident light become equal. We show that this condition can be satisfied simultaneously for many wavelengths. We demonstrate numerically and experimentally that this allows a surface plasmon resonance that extends over a broad wavelength range. We consider two methods of excitation of such broadband surface plasmon resonance: (i) patterning the interface where the surface plasmon propagates and (ii) broadband coupling through dispersion compensation. We demonstrate extremely broadband surface plasmon excitation at the Au-water or Au-air interface that extends through the whole near-infrared range from λ = 1 μm to 3 μm. We show how this broadband surface plasmon can be used for sensitive spectroscopic sensing, in particular for monitoring wetting/dewetting processes such as thin liquid film growth.