A compact laser-electron storage ring (LESR) is proposed for electron beam cooling or x-ray generation. The LESR uses an intense laser pulse stored in a high-finesse resonator to interact repetitively with a circulating electron beam in the energy range from a few MeV to a few hundred MeV. The rapid damping caused by laser-electron interaction counterbalances the intrabeam scattering effect, thus allowing electron beams with relatively low energy to be cooled or stabilized in the storage ring to very low transverse emittances. Intense x rays are produced simultaneously from Compton backscattering and can be used for x-ray lithography and other applications.