We have developed a new technique for tracking white-light coronal intensity features and have used this technique to construct continuous height/time maps of coronal ejecta as they move outward through the 2--30 Rs field of view of the Large-Angle Spectrometric Coronagraph (LASCO) on the Solar and Heliospheric Observatory (SOHO) spacecraft. Displayed as gray-scale images, these height/time maps provide continuous histories of the motions along selected radial paths in the corona and reveal a variety of accelerating and decelerating features, including two principal types of coronal mass ejections (CMEs): (1) Gradual CMEs, apparently formed when prominences and their cavities rise up from below coronal streamers: When seen broadside, these events acquire balloon-like shapes containing central cores, and their leading edges accelerate gradually to speeds in the range 400--600 km/s before leaving the 2--30 Rs field of view. The cores fall behind with speeds in the range 300--400 km/s. Seen along the line of sight, these events appear as smooth halos around the occulting disk, consistent with head-on views of optically thin bubbles stretched out from the Sun. At the relatively larger radial distances seen from this head-on perspective, gradually accelerating CMEs fade out sooner and seem to reach a constant speed more quickly than when seen broadside. Some suitably directed gradual CMEs are associated with interplanetary shocks and geomagnetic storms. (2) Impulsive CMEs, often associated with flares and Moreton waves on the visible disk: When seen broadside, these CMEs move uniformly across the 2--30 Rs field of view with speeds typically in excess of 750 km/s. At the relatively larger radial distances seen from a head-on perspective, impulsive events tend to have a more ragged structure than the gradual CMEs and show clear evidence of deceleration, sometimes reducing their speeds from 1000 to 500 km/s in 1 hour. Such decelerations are too large to represent ballistic motions in the Sun's gravitational field but might be caused by shock waves, sweeping up material far from the Sun.