During the 7-year period of the current solar cycle, 64 geoeffective coronal mass ejections (CMEs) were found to produce major geomagnetic storms (DST < -100 nT) at the Earth. In this paper we examine solar and interplanetary properties of these geoeffective coronal mass ejections (CMEs). The observations reveal that full-halo CMEs are potential sources of intense geomagnetic activity at the Earth. However, not all full-halo CMEs give rise to major geomagnetic storms, which complicates the task of space weather forecasting. We examine solar origins of the geoeffective CMEs and their interplanetary effects, namely, solar wind speed, interplanetary shocks, and the southward component of the interplanetary magnetic field, in order to investigate the relationship between the solar and interplanetary parameters. In particular, the present study aims at ascertaining solar parameters that govern important interplanetary parameters responsible for producing major geomagnetic storms. Our investigation shows that fast full-halo CMEs associated with strong flares and originating from a favorable location, i.e., close to the central meridian and low and middle latitudes, are the most potential candidates for producing strong ram pressure at the Earth's magnetosphere and hence intense geomagnetic storms. The results also show that the intensity of geomagnetic storms depends most strongly on the southward component of the interplanetary magnetic field, followed by the initial speed of the CME and the ram pressure.