I dont actually keep lists of the animals I see in zoos, generally speaking, so these are just the ones that stick out in my mind.
MAMMALS:
Platypus (Ornithorhynchus anatinus): Healesville
Long-beaked Echidna (Zaglossus bartoni): Taronga
[I've seen loads of Short-beaked Echidnas (Tachyglossus aculeatus) as well but because they are so common in Australian zoos I don't think they should count, given Arizona Docent's stipulations in his initial post]
I'm really not sure which marsupials count either because most of those I've seen are common in Australian collections, even if not overseas in many cases, but these ones stand out I think (there's heaps of others but I can't remember them off-hand):
Greater Bilby (Macrotis lagotis): Taronga; Sydney Wildlife World
Bruijn's Pademelon (Thylogale brunii): Bukittinggi
Northern Quoll (Dasyurus hallucatus): Taronga
Tasmanian Devil (Sarcophilus harrisii): Taronga; Healesville; Melbourne
Feathertail Glider (Acrobates pygmaeus): Taronga; Sydney Wildlife World
Yellow-bellied Glider (Petaurus australis): Taronga
Hoary Bamboo Rat (Rhizomys pruinosus): Khao Kheow
Sri Lankan Giant Squirrel (Ratufa macroura): Singapore Zoo
Ghost Bat (Macroderma gigas): Sydney Wildlife World
New Caledonian Fruit Bat (Pteropus vetulus): Noumea Zoo
Ornate Fruit Bat (Pteropus ornatus): Noumea Zoo
Pacific Fruit Bat (Pteropus tonganus): Noumea Zoo; Kula Eco-Park
Samoan Fruit Bat (Pteropus samoensis): Kula Eco-Park
Bornean Slow Loris (Nycticebus menagensis): Lok Kawi
Western Tarsier (Tarsius bancanus): Lok Kawi
Proboscis Monkey (Nasalis larvatus): Lok Kawi; Singapore Zoo; Ragunan Zoo
Red-shanked Douc (Pygathrix nemaeus): Singapore Zoo; Dusit Zoo
Kloss' Gibbon (Hylobates klossii): Schumutzer Primate Centre
Bornean Clouded Leopard (Neofelis diardi): Lok Kawi
Burmese Ferret-badger (Melogale personata): Chiang Mai
Leopard Seal (Hydrurga leptonyx): Taronga
New Zealand Fur Seal (Arctocephalus forsteri): Napier Marineland
Dugong (Dugong dugon): Sydney Aquarium; Sentosa Underwater World
Bornean "Pigmy" Elephant (Elephas maximus ssp): Lok Kawi
Sumatran Rhinoceros (Dicerorhinus sumatrensis harrissoni): Lok Kawi
Fea's Muntjac (Muntiacus feae): Chiang Mai
Javan Mouse Deer (Tragulus javanicus): Taman Mini Indonesia
Sri Lankan Spotted Mouse Deer (Tragulus meminna): Singapore Zoo
[and Lesser Mouse Deer (Tragulus kanchil) and Greater Mouse Deer (Tragulus napu) in various collections in Asia]
Bawean Hog Deer (Axis kuhlii): Ragunan Zoo
Eld's Deer (Cervus eldi siamensis): Dusit Zoo
Maned Serow (Capricornis sumatraensis): Chiang Mai; Dusit Zoo; Zoo Negara
BIRDS:
Most of the endemic species from the Noumea Zoo fit the criteria, including:
Kagu (Rhynochetos jubatus)
New Caledonian Goshawk (Accipiter haplochrous)
New Caledonian Imperial Pigeon (Ducula goliath)
Cloven-feathered Dove (Drepanoptila holosericea)
Horned Parakeet (Eunymphicus cornutus)
Ouvea Horned Parakeet (Eunymphicus uvaeensis)
New Caledonian Kakariki (Cyanoramphus saisseti)
Striated Starling (Aplonis striata)
New Caledonian Friarbird (Philemon diemenensis)
New Caledonian Crow (Corvus moneduloides)
Many of the endemic species from Kula Eco-Park also fit, such as:
Fiji Goshawk (Accipiter rufitorques)
Orange Dove (Chrysoenas victor)
Golden Dove (Chrysoenas luteovirens)
Collared Lory (Vini solitarius)
Masked Shining Parrot (Prosopeia personata)
Red Shining Parrot (Prosopeia tabuensis)
Kadavu Shining Parrot (Prosopeia splendens)
Wattled Honeyeater (Foulehaio carunculatus)
New Zealand species, including:
Great Spotted Kiwi (Apteryx haastii): Willowbank
Okarito Brown Kiwi (Apteryx rowi): Willowbank
[North Island Brown Kiwi (Apteryx mantelli) is far too common to count]
Fiordland Crested Penguin (Eudyptes pachyrhynchus): Taronga
White-flippered Penguin (Eudyptula minor "albosignata"): International Antarctic Centre
[Little Blue Penguin (Eudyptula minor) is so common in Australasian zoos that I have discounted it]
Chatham Island Taiko (Pterodroma magentae): Wellington Zoo
Takahe (Porphyrio hochstetteri): Willowbank; Mt. Bruce
Australasian Bittern (Botaurus poiciloptilus): Orana Park
Black Stilt (Himantopus novaezelandiae): Queenstown Kiwi Birdlife Park
Campbell Island Teal (Anas nesiotis): Willowbank; Wellington Zoo
Auckland Island Teal (Anas aucklandica): Willowbank; Orana Park
Blue Duck (Hymenolaimus malacorhynchos): Orana Park; Willowbank
New Zealand Falcon (Falco novaeseelandiae): Willowbank; Wellington Zoo
Kakapo (Strigops habroptilus): Wellington Zoo
North Island Kaka (Nestor meridionalis septentrionalis): Auckland Zoo; Mt. Bruce; Wellington Zoo; Orana Park
South Island Kaka (Nestor meridionalis meridionalis): Orana Park; Willowbank; Dunedin Botanic Gardens aviaries
Orange-fronted Kakariki (Cyanoramphus malherbi): Dunedin Botanic Gardens aviaries
Antipodes Island Parakeet (Cyanoramphus unicolor): Wellington Zoo; Orana Park; Willowbank; Dunedin Botanic Gardens aviaries
Yellowhead (Mohoua ochrocephala): Orana Park
Tui (Prosthemadera novaeseelandiae): Auckland Zoo; Parrot Ranch
New Zealand Bellbird (Anthornis melanura): Orana Park
Stitchbird (Notiomystis cincta): Mt. Bruce
North Island Saddleback (Philesturnus carunculatus rufusater): Auckland Zoo; Orana Park
North Island Kokako (Callaeas cinerea wilsoni): Mt. Bruce
And some random other ones:
Single-wattled Cassowary (Casuarius unappendiculatus): Jong's Crocodile Farm; Bali Bird Park
Maleo (Macrocephalon maleo): Ragunan Zoo
Shoebill (Balaeniceps rex): Frankfurt Zoo; Jurong Bird Park
Javan Hawk-eagle (Spizaetus bartelsi): Ragunan Zoo; Bali Bird Park
New Guinea Harpy Eagle (Harpyopsis novaeguineae): Ragunan Zoo
Sumba Hornbill (Rhyticeros everetti): Bali Bird Park
Grey-necked Picathartes (Picathartes oreas): Frankfurt Zoo
Spangled Cotinga (Cotinga cayana): Jurong Bird Park
Twelve-wired Bird Of Paradise (Seleucidis melanoleuca): Jurong Bird Park; Bali Bird Park
King Bird Of Paradise (Cicinnurus regius):Jurong Bird Park; Bali Bird Park
Magnificent Bird Of Paradise (Cicinnurus magnificus): Bali Bird Park
REPTILES:
(I don't really keep track of reptiles very well, and I honestly wouldn't have a clue in most cases whether a species is common in zoos or not, so these are just a few that must count)
Brothers Island Tuatara (Sphenodon guntheri): Orana Park; Southland Museum
[and Common Tuatara (Sphenodon punctatus) in at least nine collections in NZ as well as at Taronga, which surely discounts them on numbers!]
Arafura File-snake (Acrochordus arafurae): Sydney Aquarium
New Caledonian Sea Snake (Laticauda saintgironsi): Noumea Aquarium
MAMMALS:
Platypus (Ornithorhynchus anatinus): Healesville
Long-beaked Echidna (Zaglossus bartoni): Taronga
[I've seen loads of Short-beaked Echidnas (Tachyglossus aculeatus) as well but because they are so common in Australian zoos I don't think they should count, given Arizona Docent's stipulations in his initial post]
I'm really not sure which marsupials count either because most of those I've seen are common in Australian collections, even if not overseas in many cases, but these ones stand out I think (there's heaps of others but I can't remember them off-hand):
Greater Bilby (Macrotis lagotis): Taronga; Sydney Wildlife World
Bruijn's Pademelon (Thylogale brunii): Bukittinggi
Northern Quoll (Dasyurus hallucatus): Taronga
Tasmanian Devil (Sarcophilus harrisii): Taronga; Healesville; Melbourne
Feathertail Glider (Acrobates pygmaeus): Taronga; Sydney Wildlife World
Yellow-bellied Glider (Petaurus australis): Taronga
Hoary Bamboo Rat (Rhizomys pruinosus): Khao Kheow
Sri Lankan Giant Squirrel (Ratufa macroura): Singapore Zoo
Ghost Bat (Macroderma gigas): Sydney Wildlife World
New Caledonian Fruit Bat (Pteropus vetulus): Noumea Zoo
Ornate Fruit Bat (Pteropus ornatus): Noumea Zoo
Pacific Fruit Bat (Pteropus tonganus): Noumea Zoo; Kula Eco-Park
Samoan Fruit Bat (Pteropus samoensis): Kula Eco-Park
Bornean Slow Loris (Nycticebus menagensis): Lok Kawi
Western Tarsier (Tarsius bancanus): Lok Kawi
Proboscis Monkey (Nasalis larvatus): Lok Kawi; Singapore Zoo; Ragunan Zoo
Red-shanked Douc (Pygathrix nemaeus): Singapore Zoo; Dusit Zoo
Kloss' Gibbon (Hylobates klossii): Schumutzer Primate Centre
Bornean Clouded Leopard (Neofelis diardi): Lok Kawi
Burmese Ferret-badger (Melogale personata): Chiang Mai
Leopard Seal (Hydrurga leptonyx): Taronga
New Zealand Fur Seal (Arctocephalus forsteri): Napier Marineland
Dugong (Dugong dugon): Sydney Aquarium; Sentosa Underwater World
Bornean "Pigmy" Elephant (Elephas maximus ssp): Lok Kawi
Sumatran Rhinoceros (Dicerorhinus sumatrensis harrissoni): Lok Kawi
Fea's Muntjac (Muntiacus feae): Chiang Mai
Javan Mouse Deer (Tragulus javanicus): Taman Mini Indonesia
Sri Lankan Spotted Mouse Deer (Tragulus meminna): Singapore Zoo
[and Lesser Mouse Deer (Tragulus kanchil) and Greater Mouse Deer (Tragulus napu) in various collections in Asia]
Bawean Hog Deer (Axis kuhlii): Ragunan Zoo
Eld's Deer (Cervus eldi siamensis): Dusit Zoo
Maned Serow (Capricornis sumatraensis): Chiang Mai; Dusit Zoo; Zoo Negara
BIRDS:
Most of the endemic species from the Noumea Zoo fit the criteria, including:
Kagu (Rhynochetos jubatus)
New Caledonian Goshawk (Accipiter haplochrous)
New Caledonian Imperial Pigeon (Ducula goliath)
Cloven-feathered Dove (Drepanoptila holosericea)
Horned Parakeet (Eunymphicus cornutus)
Ouvea Horned Parakeet (Eunymphicus uvaeensis)
New Caledonian Kakariki (Cyanoramphus saisseti)
Striated Starling (Aplonis striata)
New Caledonian Friarbird (Philemon diemenensis)
New Caledonian Crow (Corvus moneduloides)
Many of the endemic species from Kula Eco-Park also fit, such as:
Fiji Goshawk (Accipiter rufitorques)
Orange Dove (Chrysoenas victor)
Golden Dove (Chrysoenas luteovirens)
Collared Lory (Vini solitarius)
Masked Shining Parrot (Prosopeia personata)
Red Shining Parrot (Prosopeia tabuensis)
Kadavu Shining Parrot (Prosopeia splendens)
Wattled Honeyeater (Foulehaio carunculatus)
New Zealand species, including:
Great Spotted Kiwi (Apteryx haastii): Willowbank
Okarito Brown Kiwi (Apteryx rowi): Willowbank
[North Island Brown Kiwi (Apteryx mantelli) is far too common to count]
Fiordland Crested Penguin (Eudyptes pachyrhynchus): Taronga
White-flippered Penguin (Eudyptula minor "albosignata"): International Antarctic Centre
[Little Blue Penguin (Eudyptula minor) is so common in Australasian zoos that I have discounted it]
Chatham Island Taiko (Pterodroma magentae): Wellington Zoo
Takahe (Porphyrio hochstetteri): Willowbank; Mt. Bruce
Australasian Bittern (Botaurus poiciloptilus): Orana Park
Black Stilt (Himantopus novaezelandiae): Queenstown Kiwi Birdlife Park
Campbell Island Teal (Anas nesiotis): Willowbank; Wellington Zoo
Auckland Island Teal (Anas aucklandica): Willowbank; Orana Park
Blue Duck (Hymenolaimus malacorhynchos): Orana Park; Willowbank
New Zealand Falcon (Falco novaeseelandiae): Willowbank; Wellington Zoo
Kakapo (Strigops habroptilus): Wellington Zoo
North Island Kaka (Nestor meridionalis septentrionalis): Auckland Zoo; Mt. Bruce; Wellington Zoo; Orana Park
South Island Kaka (Nestor meridionalis meridionalis): Orana Park; Willowbank; Dunedin Botanic Gardens aviaries
Orange-fronted Kakariki (Cyanoramphus malherbi): Dunedin Botanic Gardens aviaries
Antipodes Island Parakeet (Cyanoramphus unicolor): Wellington Zoo; Orana Park; Willowbank; Dunedin Botanic Gardens aviaries
Yellowhead (Mohoua ochrocephala): Orana Park
Tui (Prosthemadera novaeseelandiae): Auckland Zoo; Parrot Ranch
New Zealand Bellbird (Anthornis melanura): Orana Park
Stitchbird (Notiomystis cincta): Mt. Bruce
North Island Saddleback (Philesturnus carunculatus rufusater): Auckland Zoo; Orana Park
North Island Kokako (Callaeas cinerea wilsoni): Mt. Bruce
And some random other ones:
Single-wattled Cassowary (Casuarius unappendiculatus): Jong's Crocodile Farm; Bali Bird Park
Maleo (Macrocephalon maleo): Ragunan Zoo
Shoebill (Balaeniceps rex): Frankfurt Zoo; Jurong Bird Park
Javan Hawk-eagle (Spizaetus bartelsi): Ragunan Zoo; Bali Bird Park
New Guinea Harpy Eagle (Harpyopsis novaeguineae): Ragunan Zoo
Sumba Hornbill (Rhyticeros everetti): Bali Bird Park
Grey-necked Picathartes (Picathartes oreas): Frankfurt Zoo
Spangled Cotinga (Cotinga cayana): Jurong Bird Park
Twelve-wired Bird Of Paradise (Seleucidis melanoleuca): Jurong Bird Park; Bali Bird Park
King Bird Of Paradise (Cicinnurus regius):Jurong Bird Park; Bali Bird Park
Magnificent Bird Of Paradise (Cicinnurus magnificus): Bali Bird Park
REPTILES:
(I don't really keep track of reptiles very well, and I honestly wouldn't have a clue in most cases whether a species is common in zoos or not, so these are just a few that must count)
Brothers Island Tuatara (Sphenodon guntheri): Orana Park; Southland Museum
[and Common Tuatara (Sphenodon punctatus) in at least nine collections in NZ as well as at Taronga, which surely discounts them on numbers!]
Arafura File-snake (Acrochordus arafurae): Sydney Aquarium
New Caledonian Sea Snake (Laticauda saintgironsi): Noumea Aquarium