Using the Dst value corrected for the effects of magnetopause currents (Dst*) and solar wind magnetic field and plasma data from 1 January 1998 to 30 April 2002, during elevated solar conditions, we have statistically examined the relationship of 271 storms (Dst* ≤ -30 nT) to 104 magnetic clouds. It is found that most of the magnetic clouds result in geomagnetic storms, but only about 30% of storms are due to magnetic clouds. A storm can be driven by a cloud's various regions or their combinations with dissimilar occurrence percentages. These percentages change as a function of geomagnetic activity levels as well. It is found that the leading field is the most geoeffective region and the sheath region is equally effective at causing magnetic storms during solar maximum (42%) compared to solar minimum (43%) as a percentage of magnetic cloud-induced storms. The occurrence percentage of intense storms caused by clouds is 72%, which is much higher than the ~20% occurrence percentage of smaller storms caused by clouds. It is also found that unipolar Bz and bipolar Bz clouds have different geoeffectiveness percentages, depending on the Bz orientation. The long-known control of magnetic activity mainly by southward Bz is supported by the results of this study. It is also shown that multistep development storms can result not only from both the combinations of sheath and cloud fields but also from different fields within a cloud. A new name, quasi-cloud, is proposed for those cloud-like solar wind structures which show evidence of relatively organized field rotations.