Gap surface plasmon (GSP) modes, the localized electromagnetic modes existing between two metal structures separated by a nano-gap, are able to support subwavelength confinement and enhancement of a light field upon resonance excitation. Such features can greatly facilitate various light-matter interactions at the nanoscale. Here, we demonstrate a planar nano-gap architecture existing between a pair of tip-shaped gold pads. The nano-gap gives rise to plasmon resonances with strong light confinement close to the tip surfaces in the visible to near-infrared spectral region. Accordingly, we showed that the plasmonic gold nano-gap can exhibit strong intrinsic second-harmonic generation (SHG) and significantly enhance the Raman scattering signal from small molecules. Furthermore, by arranging the nano-gap into arrays, a stronger SHG signal can be obtained. In addition, the surface enhanced Raman scattering (SERS) activity is also improved by two orders of magnitude compared to that of a single nano-gap. Overall, the findings in our study have demonstrated the potential applications of a plasmonic nano-gap and its arrays for signal generation and sensitive chemical sensing at the nanoscale.