We report in this paper the near-field microscopic studies on localized plasmon resonances in gold nanoparticles and their assemblies (nanorods, triangular nanoplates, and assembled nanospheres). We have utilized near-field measurements of linear transmission/scattering, as well as nonlinear two-photon excitation, to enable spectroscopic imaging of local electric field or local density of electromagnetic states. We show that the wavefunction of the plasmon excitation in the nanoparticle is visualized by the near-field methods. For single nanorod, many plasmon resonances were observed in the near-field transmission spectrum. At each resonant peak wavelength, the near-field image of the nanorod gave a characteristic spatially oscillating feature along the long axis of the nanorod. The feature is attributable to the square modulus of the resonant plasmon-mode wavefunction. In the assembled nanoparticles, strong electric-field enhancement localized in the interstitial sites ("hot spot"), which was theoretically predicted previously, was clearly imaged by the near-field two-photon excitation method. Major contribution of the hot spots to surface enhanced Raman scattering is also shown for the samples weakly doped with Raman-active dye molecules, by the near-field excited Raman spectra and images.