Plasmonic resonances in multiple systems are theoretically investigated with a first principles approach. The plasmonic behaviors of doped semiconductor nanocrystals are explored with a quantum TDLDA approach and a classical hybridization theory. The origins and properties of plasmonic resonances from a wide variety of physical systems are explored using rigorous quantum mechanical computations. A universal metrics, the generalized plasmonicity index, is proposed to classify plasmonic resonances from other optical resonances. Using the generalized plasmonicity index, the plasmonicity of optical resonances in multiple systems are quantified, including jellium spheres, atomic-scale metallic clusters, nanostructured graphene, and polycyclic aromatic hydrocarbons. The generalized plasmonicity index provides a rigorous way to quantify the plasmonic behaviors in ultra-small systems. It also offers a quantitative foundation for the design of devices based on molecular plasmonics.