We address the question whether there exist sympathetic coronal mass ejections (CMEs), which take place almost simultaneously in different locations with a certain physical connection. For this study, the following three investigations are performed. First, we have examined the waiting-time distribution of the CMEs that were observed by the SOHO Large Angle and Spectrometric Coronagraph (LASCO) from 1999 February to 2001 December. The observed waiting-time distribution is found to be well approximated by a time-dependent Poisson distribution without any noticeable overabundance at short waiting times. Second, we have investigated the angular difference distribution of successive CME pairs to examine their spatial correlations. A remarkable overabundance relative to background levels is found within 10° of the position angle difference, which supports the existence of quasi-homologous CMEs that occur sequentially in the same active region. Both of the above results indicate that sympathetic (interdependent) CMEs are far less frequent than independent CMEs. Third, we have examined the EUV Imaging Telescope running difference images and the LASCO images of quasi-simultaneous CME pairs and found a candidate sympathetic CME pair, of which the second CME may be initiated by the eruption of the first CME. Possible mechanisms of the sympathetic CME triggering are discussed.