We report systematic measurements of Raman scattering by electrons in elemental metals Al, Mo, Nb, Os, Pb, Re, Ta, Ti, V, W, and metallic compound LaB6. Experimental spectra are modeled on the base of the band structures, calculated within the density functional theory, taking properly into account the effects of electron-phonon scattering. The agreement between our measured and calculated spectra is excellent for the variety of metals, thus providing information on the electron self-energies and estimates for the electron-phonon coupling constants and temperature-dependent relaxation rates. The method can be applied to other metallic materials to evaluate an electron-phonon coupling as an alternative to transport and optical measurements.