Observations of the solar corona with the LASCO and EIT instruments on SOHO provide an unprecedented opportunity to study coronal mass ejections (CMEs) from their initiation through their evolution out to 30 R⊙. The objective of this study is to gain an understanding of the source regions from which the CMEs emanate. To this end, we have developed a list of 32 CMEs whose source regions are located on the solar disk and are well observed in EIT 195 Å data during the solar minimum phase of January 1996-May 1998. We compare the EIT source regions with photospheric magnetograms from the Michelson Doppler Imager (MDI) instrument on SOHO and the NSO/Kitt Peak Observatory and also with Hα data from various sources. The overall results of our study show that 59% of the CME related transients observed in EIT 195 Å images are associated with active regions without prominences, 22% are associated with eruptions of prominences embedded in active regions and 19% are associated with eruptions of quiescent prominences. We describe 3 especially well observed events, one from each of these 3 categories. These case studies suggest that active region CMEs are associated with active regions with lifetimes between 11-80 days. They are also often associated with small scale emerging or cancelling flux over timescales of 6-7 hours. CMEs associated with active region prominence eruptions, on the other hand, are typically associated with old active regions with lifetimes ~ 6-7 months.