We examine the contributions of the principal solar wind components (corotating high-speed streams, slow solar wind, and transient structures, i.e., interplanetary coronal mass ejections (CMEs), shocks, and postshock flows) to averages of the aa geomagnetic index and the interplanetary magnetic field (IMF) strength in 1972--2000 during nearly three solar cycles. A prime motivation is to understand the influence of solar cycle variations in solar wind structure on long-term (e.g., approximately annual) averages of these parameters. We show that high-speed streams account for approximately two-thirds of long-term aa averages at solar minimum, while at solar maximum, structures associated with transients make the largest contribution (~50%), though contributions from streams and slow solar wind continue to be present. Similarly, high-speed streams are the principal contributor (~55%) to solar minimum averages of the IMF, while transient-related structures are the leading contributor (~40%) at solar maximum. These differences between solar maximum and minimum reflect the changing structure of the near-ecliptic solar wind during the solar cycle. For minimum periods, the Earth is embedded in high-speed streams ~55% of the time versus ~35% for slow solar wind and ~10% for CME-associated structures, while at solar maximum, typical percentages are as follows: high-speed streams ~35%, slow solar wind ~30%, and CME-associated ~35%. These compositions show little cycle-to-cycle variation, at least for the interval considered in this paper. Despite the change in the occurrences of different types of solar wind over the solar cycle (and less significant changes from cycle to cycle), overall, variations in the averages of the aa index and IMF closely follow those in corotating streams. Considering solar cycle averages, we show that high-speed streams account for ~44%, ~48%, and ~40% of the solar wind composition, aa, and the IMF strength,, respectively, with corresponding figures of ~22%, ~32%, and ~25% for CME-related structures, and ~33%, ~19%, and ~33% for slow solar wind.