We report on the direct measurement of dispersion relations of plasmons confined in atomically thin metal films and wires by electron energy loss spectroscopy in wide energy-momentum range. Ultrathin Ag films are prepared on single crystal Si surfaces by molecular beam epitaxy, and its crystallinity is checked by electron diffraction. For the case of multi-atomic-layer Ag films, two plasmon modes are observed at around 3.9 eV and 1.8 eV which are localized at the top and the bottom surfaces of the films, respectively. For the case of Ag monoatomic layer, a single mode is observed that steeply disperses in the mid-infrared range. Nonlocal and quantum effects are found to be essential in understanding its full plasmon dispersion curve up to the critical wave number of Landau damping. For the case of Au atom chains, an anisotropic sound-wave-like plasmon dispersion is found that clearly shows ID plasmon confinement in each atom chain.