Electron-spin resonance of the rare-earth ions ${\mathrm{Ce}}^{+3}$, ${\mathrm{Dy}}^{+3}$, ${\mathrm{Er}}^{+3}$, and ${\mathrm{Yb}}^{+3}$ has been observed in various cubic intermetallic compounds. Our experimental results indicate the ground states to be (a) ${\ensuremath{\Gamma}}_{7}$ for ${\mathrm{Yb}}^{+3}$ in La${\mathrm{Pd}}_{3}$ (${\mathrm{Cu}}_{3}$Au structure), (b) ${\ensuremath{\Gamma}}_{8}^{(1)}$ for ${\mathrm{Er}}^{+3}$ in LaSb, LuSb, LaBi, and LuBi (NaCl structure), (c) ${\ensuremath{\Gamma}}_{7}$ for ${\mathrm{Ce}}^{+3}$ in LaSb, (d) ${\ensuremath{\Gamma}}_{6}$ for ${\mathrm{Dy}}^{+3}$ in LaSb, (e) ${\ensuremath{\Gamma}}_{6}$ for ${\mathrm{Yb}}^{+3}$ in LaSb, and (f) ${\ensuremath{\Gamma}}_{6}$ for Er in La${\mathrm{B}}_{6}$ (Ca${\mathrm{B}}_{6}$ structure). These data represent the first observations of anisotropic resonance and hyperfine structure in intermetallic compounds as well as the first observation of EPR of ${\mathrm{Ce}}^{+3}$ in any metal. The observations are consistent with crystalline field parameters deduced from measurements of concentrated spin systems with the same structure, by means of other experimental techniques. Analysis of the crystalline field parameters in terms of the point-charge model, the virtual-bound-state model, and possible $f$-like contributions is given.