It all depends on regions. Many North Americans will mention the North American river otter and sandhill crane, which I have personally never seen. For Aussies, koalas and kiwis may be stock animals while they're pretty rare in Europe. Meanwhile, Europeans consider raccoons typical zoo animals, while Americans see them as pests. I've seen quite some animals mentioned here (Eurasian wild boar, barbary macaque, vicuña and wapiti come to mind) that I don't recall ever seeing in zoos despite having visited quite a number in Europe, Brazil and Singapore.I see chevrotain and shoebill mentioned here a lot but as far as I know they are anything but common nor basic.
What I don’t see enough is however are vicuña and Eurasian white storks.
From my experience in Singapore (and I assume this goes for much of Southeast Asia), chevrotains and crowned pigeons are among the most common zoo animals as they are easy to keep, fit in with other animals and are especially great to display in walkthrough aviaries/jungle domes.