In that late 1800's Great Spotted, Little Spotted and Southern Brown Kiwi's were all imported to various facilities in Europe. Although I can't find anything on it, I would not be surprised if some had been imported to America around the same time as well.
for endemics or near-endemics, outside New Caledonia there are kagu, cloven-feathered dove, goliath imperial pigeon, horned parakeet, New Caledonian crow, red-throated parrotfinch, and most of the reptile species. I only know of the goliath imperial pigeon being in Japan and the cloven-feathered dove in private hands in Europe. There have been New Caledonian crows in zoos but I think they are now all in non-zoo facilities. all protected wildlife in NZ can only be held under permit. It is not the decision of the zoos whether they can or can't export protected wildlife. Basically the reasons for holding them in captivity is if it is of benefit to the species, or for rescue/rehab purposes. A foreign zoo simply wanting tui because they are common in NZ is not a valid reason.
I believe there's still an individual kept in Walsrode (Germany) but he's mostly off-show these days.
+ its close relative the Ouvea parakeet, but it is much rarer and as far as I know none in North America. Among the New Caledonian reptiles, a few are common in captivity, both privately and in zoos: gargoyle, crested and New Caledonian giant geckos, but there are also smaller numbers of some of the others geckos. It seems there is very little interest (by zoos or privates) in the skinks from New Caledonia and consequently they're virtually absent from captivity. This "popular gecko vs. unpopular skink" pattern is mirrored by the New Zealand species, though there are far fewer New Zealand geckos than New Caledonian geckos in captivity. There has been no mention of fish in earlier posts, but a review of what is kept outside the native range can be done quite fast: None of the relatively few freshwater fish species of New Zealand and New Caledonia are kept elsewhere. None of New Caledonia's endemic marine fish are kept elsewhere, but species that are found more widely in the Coral Sea are fairly regular in coral reef aquariums. I'm only aware of a single aquarium outside New Zealand with endemic/near-endemic marine fish from that country: Osaka (Japan) has fairly big Cook Strait aquarium with quite a range of species. There are a few old-ish photos from the tank here (the tank now also holds loggerhead sea turtle). BTW, contrary to the suggestion in the first post of this thread, the New Caledonian crow is not the only species of corvid that has been observed to use tools in the wild. It is, however, by far the one where tool use has been most extensively studied and seemingly also the one that uses it most frequently. You don't have to leave your homestate of Texas to see corvids that are known to use tools: American crow and green jay.
I was sure I had read on here that the Walsrode bird had gone back to the collection it had come from, but I just trawled through the last couple of Walsrode threads to find the post and discovered that I had remembered it wrong. The post said "It was an ancient bird from a private collection. It is now off-show I believe."
I know in the past a lot of galaxiids and bullies have been exported from NZ to private aquarists in Germany. No idea on the current situation with them over there though. In one of the Chinese aquariums I saw a Southern Pigfish Congiopodus leucopaecilus [NZ and southern Australia] which really surprised me.
As far as I know, they're gone. For European aquarists with an interest in colder-water gobies and alike it seems there has been a shift towards Chinese species. Last I heard was in the low tens in Europe, but this was based on rather uncertain information, especially for France and the Czech Republic. France has historically been in the forefront of keeping of NC species due to its close connection with the archipelago, and the Czech Republic is a center of parrot keeping and breeding in Europe. Czech CITES register showed 152 (!) horned parakeets in the country in 2015, but this may include some Ouvea as it is considered a subspecies in the taxonomy used by CITES. Anyway, at least some of the Ouvea that do remain are offspring of the c. 10 birds that were imported to Germany in the 80s and early 90s. As far as I know, the only Ouvea in a zoo outside its native range are at Loro Parque (Tenerife, Spain) where it also has bred. I'm not aware of any in North America (certainly none in zoos), but there might be a few kept privately.
There are still some Ouvea around, but unlike Horned parakeets they are extremely rare. Low tens would be my guess as well. There might be some in Germany, Netherlands and Belgium as well. Horned parakeets are getting more common. The European population breeds quite well. And most Kagu in Europe are still in private hands as well although it is only one breeder in France.