We investigate geomagnetic storm activity during periods of 135 magnetic clouds identified with hourly averages of OMNI data from 1965 to 1998. It is found that the storm Dst index correlates well with both the Bz component (correlation coefficient, c.c. = -0.86) and the rectified electric field VBS (c.c. = -0.88) but does not correlate well with solar wind speed (c.c. = -0.58), indicating that the role of magnetic cloud speed in predicting storm intensity is a minor one. Solar wind speed does become important in predicting Dst for the studied cloud events when high solar wind speeds are considered. The correlation coefficient (c.c.) for Dst versus Bz increases dramatically when the solar wind speed exceeds 600 km/s. For example, the c.c. for Dst versus Bz is 0.99 for speeds between 600 and 750 km/s (15 events). This implies that solar wind velocity is also important indirectly for predicting the storm intensity when using Bz as a direct predictor. Specially, over the next 2 or 3 years, cloud speed is expected to increase, on average, as has already been observed. This provides us a good opportunity to estimate the intensity of cloud-associated geomagnetic storms by using the observed upstream Bz.