Many animals seem to have poor mental health in zoos, and bears, gorillas, penguins, tigers, and others are given anti-depressants and/or anti-anxiety drugs [0-4]. Repetitive behaviors, e.g., the back and forth pacing behavior of carnivores or swimming continually in a circle, is supposedly a sign of psychosis caused by confinement. An environment free from danger without the threat of hunger seems to lead to mental health problems in these animals.

That said, I think zoos are critical to educating the public about animals, preserving endangered species, enabling injured animals to live, and making people care about animals from an early age.

[0] https://www.wired.com/2014/07/animal-madness-laurel-braitman...

[1] https://www.peta.org.uk/blog/why-are-these-penguins-taking-a...

[2] http://www.onegreenplanet.org/animalsandnature/why-do-polar-...

[3] http://www.toledoblade.com/frontpage/2005/09/12/Zoos-using-d...

[4] http://www.slate.com/blogs/wild_things/2014/06/20/animal_mad...