The electronic and optical properties of colloidal quantum dots, including the wavelengths of light that they can absorb and emit, depend on the size of the quantum dots. These properties have been exploited in a number of applications including optical detection(1-3), solar energy harvesting(4,5) and biological research(6,7). Here, we report the self-assembly of quantum dot complexes using cadmium telluride nanocrystals capped with specific sequences of DNA. Quantum dots with between one and five DNA-based binding sites are synthesized and then used as building blocks to create a variety of rationally designed assemblies, including cross-shaped complexes containing three different types of dots. The structure of the complexes is confirmed with transmission electron microscopy, and photophysical studies are used to quantify energy transfer among the constituent components. Through changes in pH, the conformation of the complexes can also be reversibly switched, turning on and off the transfer of energy between the constituent quantum dots.