In Mott insulators with the t^4_{2g} electronic configuration such as of Re^{3+}, Ru^{4+}, Os^{4+}, and Ir^{5+} ions, spin-orbit coupling dictates a Van Vleck-type nonmagnetic ground state with angular momentum J=0, and the magnetic response is governed by gapped singlet-triplet excitations. We derive the exchange interactions between these excitons and study their collective behavior on different lattices. In perovskites, a conventional Bose condensation of excitons into a magnetic state is found, while an unexpected one-dimensional behavior supporting spin-liquid states emerges in honeycomb lattices, due to the bond-directional nature of exciton interactions in the case of 90 degree d-p-d bonding geometry.