A high-resolution neutron spectroscopic technique is used to measure momentum-resolved magnon lifetimes in the prototypical two- and three-dimensional antiferromagnets Rb(2)MnF(4) and MnF(2), over the full Brillouin zone and a wide range of temperatures. We rederived theories of the lifetime resulting from magnon-magnon scattering, thereby broadening their applicability beyond asymptotically small regions of wave vector and temperature. Corresponding computations, combined with a small contribution reflecting collisions with domain boundaries, yield excellent quantitative agreement with the data. Comprehensive understanding of magnon lifetimes in simple antiferromagnets provides a solid foundation for current research on more complex magnets.