We discuss spin-S antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary S. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-2S SU(2) Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of S=1 and S=3/2 systems by using exact diagonalization and level spectroscopy.