We investigate geomagnetic activity associated with magnetic clouds as well as some aspects of the clouds' magnetic field structure (e.g., magnetic field distributions of the clouds). Thirty-four magnetic cloud events observed by Wind over the years 1995--1998 are investigated in this study. Magnetic clouds are a principal source of strong, long-lasting, interplanetary, negative Bz fields (in solar magnetospheric coordinates) and hence are a major source of geomagnetic activity (Dst < -50 nT). The region just upstream of a cloud may be a significant source of southward fields instead of, or as well as, the cloud itself. We call this upstream region a sheath if it is bounded by a shock (or a pressure pulse) and the cloud. This study helps to identify the major sources (regions of southward Bz following shock passages or within the magnetic clouds) that are most dominant in the generation of geomagnetic storms. It is found that a geomagnetic storm can be induced by (1) a sheath, (2) the leading (i.e., front part) region of a cloud, (3) the trailing part of a cloud, and (4) both sheath and cloud regions. (Because of this complexity a storm with a multistep main phase can occur.) The related occurrence percentages of storms were 17.6% (six events), 44.1% (15 events), 5.9% (two events), and 20.6% (seven events), and the averaged storm intensities (minimum Dst) were -60, -85, -92, and -58 nT, respectively. For the remaining four events (11.8%), there were no storms. The occurrence timing of storm intensity is highly correlated with the occurrence timing of minimum Bz (maximum VBs or ε) for a magnetic cloud with the field rotating from southward to northward.