We show that the strongly spin-orbit coupled materials Bi2Te3 and Sb2Te3 and their derivatives belong to the Z2 topological-insulator class. Using a combination of first-principles theoretical calculations and photoemission spectroscopy, we directly show that Bi2Te3 is a large spin-orbit-induced indirect bulk band gap (delta approximately 150 meV) semiconductor whose surface is characterized by a single topological spin-Dirac cone. The electronic structure of self-doped Sb2Te3 exhibits similar Z2 topological properties. We demonstrate that the dynamics of spin-Dirac fermions can be controlled through systematic Mn doping, making these materials classes potentially suitable for topological device applications.