Quite a few species in private hands here in the states. I've never kept any but would love to when I can manage the space and time for it.
Off the top of my head, Toco, Keel-billed, Red-billed, Channel-billed, and Chestnut-mandibled Toucans, Green and Curl-crested Aracaris, all fairly regularly seen and a good deal of breeding. Handful of other species also around, in small numbers.
Far as hornbills, Red-billeds and Yellow-billeds of some species, African Gray, Silvery-cheeked, and Trumpeter are most common. I have seen a couple species of large Asian hornbill and the Southern Ground Hornbill offered for sale before, although I think most of those go to zoos.