Parrots and dogs will tear apart their environments (and sometimes their bodies) under certain circumstances, such as extended loneliness. Seems similar to human depression.

Yes, my housemate's dog has separation anxiety which is not good (but he was adopted from a shelter).

We hypothesize he gets all anxious because when we are leaving and locking him in his (reinforced) cage - he doesn't know if we'll ever return. Which is different from humans - as in we know that it is only a matter of time.

This review, and its references, are a little dated, so I presume that the animal models are much more sophisticated by now:

http://dx.doi.org/10.1111/j.1440-1819.1990.tb00461.x