Superconductivity and ferromagnetism are antagonistic forms of order, and rarely coexist. Many interesting new phenomena occur, however, in hybrid superconducting/ferromagnetic systems. For example, a Josephson junction containing a ferromagnetic material can exhibit an intrinsic phase shift of pi in its ground state for certain thicknesses of the material. Such "pi-junctions" were first realized experimentally in 2001, and have been proposed as circuit elements for both high-speed classical superconducting computing and for quantum computing. Here we demonstrate experimentally that the phase state of a Josephson junction containing two ferromagnetic layers can be toggled between 0 and pi by changing the relative orientation of the two magnetizations. These controllable 0-pi junctions have immediate applications in cryogenic memory where they serve as a necessary component to an ultra-low power superconducting computer. Such a fully superconducting computer is estimated to be orders of magnitude more energy-efficient than current semiconductor-based supercomputers. Phase controllable junctions also open up new possibilities for superconducting circuit elements such as superconducting "programmable logic," where they could function in superconducting analogs to field-programmable gate arrays.