According to some scientists and philosophers of science, a theory is or should be judged by its ability to make successful predictions. This paper examines a case from the history of recent science—the research of Hannes Alfvén and his colleagues on space plasma phenomena—in order to see whether scientists actually follow this policy. Tests of five predictions are considered: magnetohydrodynamic waves, field-aligned (“Birkeland”) currents, critical ionization velocity and the existence of planetary rings, electrostatic double layers, and partial corotation. It is found that the success or failure of these predictions had essentially no effect on the acceptance of Alfvén's theories, even though concepts such as “Alfvén waves” have become firmly entrenched in space physics. Perhaps the importance of predictions in science has been exaggerated; if a theory is not acceptable to the scientific community, it may not gain any credit from successful predictions.