I was given a small clipping of this plant and it is really taking off. Does anyone know what family this is?
I believe that's Chinese Stonecrop.
I think we're having a hard time pinning it down because this species is most commonly seen today in the form of it's red-leaf-tipped cultivar "Coral Reef Stonecrop."
My double-checking on this has led me to conclude the "Coral Reef" cultivar became so much more popular than the original that the cultivar name supplanted the real name.
This doesn't look like Purslane to me, black thumb. I know it can get quite weedy, but it can be, and is grown as a house plant, which if controlled, is workable. I have one at home.
I think this plant up here is a species or species hybrid of Crassula.
Update: It appears to be a species of Pilea or Sedum.