One I forgot to mention is Sugar gliders. They are very common as pets and can be fed a commercial diet, fruit and mealworms. They are often kept in fairly small cages, however some keep them in aviaries. Sugar gliders cannot be litter trained either.
Short-tailed opossums are also quite common in the pet trade and in America, I believe many people keep Virginia opossums. Brush tail possums are not very common (but they do exist in private collections) due to them not being rare in the pet trade and expensive, they also are very aggressive and have sharp claws. According to some accounts, they can be fairly gentle however now there are many bans on importing them, so it is extremely difficult to get hold of one. The enclosure size would have to be quite large and they typically eat leaves, bark and a few other foods when kept as pets.
Ringtails can scratch and bite and I haven't seen them much in private collections, however I have noticed many people keep them in outdoor aviaries usually in petting zoos. They breed easily as well.
Quolls are quite rare and I have not heard of any breeders or private collectors outside of Australia. They are very aggressive as well.
Bettongs - mainly Brush-tailed bettongs - are fairly common in America and they are quite gentle, although sometimes destructive.