The Deutsch-Jozsa Algorithm, while not immediately "practical" in the sense that it solved some real-world problem that had been vexing computer scientists, was instrumental in showing conclusively that quantum computers could be asymptotically faster than classical computers for some problems. This then led the way for more applied quantum algorithms such as Shor's Algorithm (itself a special case of QFT and period-finding algorithms). So I'd like to nominate DJA for an algorithm that changed the world.