It looks like a trunk-forming Opuntia (prickly pear cactus) of some sort; perhaps Opuntia brasiliensis (syn. Brasiliopuntia brasiliensis). I base this on the fact that the pads are separated from the trunk by branch-like extensions, giving it the look of a "normal" tree. Compare here and here.
Thanks for the help! My plant does look very much like the second referenced photo in your reply, the one from rschoi.com.ne.kr. We have never seen any flower or fruit develop on this plant. Is that consistent with opuntias (opuntii?)? Many of the references to opuntias link it to prickly pear cactus which usually do flower. Any other info you have or can direct me to would be appreciated.
Many of the visitors to my office that expressed interest in the plant have taken "leaves" and report virtually unanamous success in getting a new plant started.
