The rich structure of bright and dark surface-plasmon modes localized in individual and coupled gold nanoparticles is unveiled by electron-energy-loss spectroscopy performed in a scanning transmission electron microscope. Spatially resolved maps of surface-plasmon modes in the approximately 1.5-2.5 eV range (wavelengths approximately 500-800 nm), collected for individual nanorods, coupled nanorod dimers, and touching nanosphere dimers, are in excellent agreement with theory. Surface-plasmon maps constructed from the spatially and spectrally resolved energy-loss signals are shown to mimic rather well the near fields calculated for external illumination in the case of bright surface-plasmon modes (i.e., those coupling to external light). Dark surface-plasmon modes that cannot be excited by optical means are also found, and our electron probing technique provides further insight into their corresponding spatial distribution and symmetry, which are not accessible to any other existing techniques. Our results initiate the study of a whole set of new dark surface-plasmon modes that should become a source of new applications in sensing and microscopy but have escaped experimental scrutiny so far.