The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.