I see this is a very popular thread and very regional. Our UK friends list many species that we here in the US take for granted (one example: it seems the majority of zoos here with wolves have mexican wolves, which I've seen many times). A common theme is Australian animals, not surprising due to their uniqueness and due to EXTREMELY stringent export regulations on the part of the Aussie government.
Kakapo mentions "boat-billed heron." We have those in our South America aviary here at Reid Park Zoo, very easy to see (except of course for the long flight from Spain to Arizona).
A few mentions of various crocodiles; I believe St Augustine Alligator Farm in northern Florida has every species of crocodilian in the world (never been there myself, but it seems that's what they used to claim).
Also a couple California Condor mentions. Years ago, San Diego Wild Animal Park finally put their condors on public display. This summer, the San Diego Zoo will also have them as part of the new Elephant Odyssey. Also, Santa Barbara Zoo is building a new condor exhibit.
Condors were strictly off-exhibit until their numbers finally got high enough. Maybe the same will happen with iberian lynx that a couple people mention (and is a top on my list as a cat fanatic). Their numbers are increasing in captivity, there will be six breeding centers by the end of this year, and Zoo Jerez has them off exhibit. Maybe Zoo Jerez will be allowed to build a public display in a couple years?