We determine the solar wind structures (coronal mass ejection (CME)-related, corotating high-speed streams, and slow solar wind) driving geomagnetic storms of various strength over nearly three solar cycles (1972–2000). The most intense storms (defined by Kp) at both solar minimum and solar maximum are almost all (∼97%) generated by transient structures associated with CMEs. Weaker storms are preferentially associated with streams at solar minimum and with CMEs at solar maximum, reflecting the change in the structure of the solar wind between these phases of the solar cycle. Slow solar wind generates a small fraction of the weaker storms at solar minimum and maximum. We also determine the size distributions of Kp for each solar wind component.