great white, blue, greater hammerhead, bull, and mako sharks.
There are major differences in the difficulties of keeping those species. Great white can be done but it is evidently very hard and there are few places with large enough exhibits of the right temperature, i.e. subtropical to warm temperate. Additionally, based on the attempts by Monterey, they start to exhibit predatory aggressive behavior towards reasonably sized animals quite early, so you could end up with a huge exhibit with only a single inhabitant. Sure other larger sharks kept in captivity do on occasion eat a co-inhabitant, but it can typically be managed with regular feeding. Interestingly, the whitetip reef shark, a shark that only reaches a moderate size and generally isn't considered all that aggressive, is sometimes quite unmanageable in captivity, basically having a go at anything during their nightly prowls: Small fish, medium fish, other sharks. Sourcing a great white would also be extremely hard (and arguably questionable considering their status).
Blue and mako are true pelagic sharks and the few places that have tried did not result in any successes. So far they belong in the essentially impossible category.
Great hammerhead is comparably to scalloped, i.e. difficult but doable. When reaching a reasonable size, both do have tendencies to snack on rays, which can present a problem. Georgia learned that the hard way (try searching "Death at the Georgia Aquarium" on youtube). Yes, this species is still kept at Atlantis.
Bull shark is comparable to most
Carcharhinus that have been tried, i.e. reasonably straight forward. Bull sharks have been maintained in captivity for a very long time (decades in a few cases), including breeding.
The following large, predatory free-swimming sharks of warmer waters all do reasonably well in captivity:
Carcharhinus,
Negaprion, sand tiger and hammerheads. Of these groups, only the larger hammerheads still haven't been bred in captivity, but in the last few years several aquariums have been set up with the hope of eventual success for scalloped.
Tiger shark is a bit of a hit-and-miss, but based on results at a few aquariums in the last decade it does not belong in the "impossible" category as once believed.
Most botoom-living sharks also do quite well, e.g. wobbegongs, nurse sharks, zebra, whitetip reef, etc. Unless things changes, sawfish are on the way out. There is only a single case of captive breeding, and now where Australia has decided against exporting, there are no places where they can be sourced legally. Australia was the only place where CITES export grants were available because of the reasonably large populations in that country (unlike pretty much everywhere else). The much smaller sawsharks are fairly similar and overall much more common, but don't seem to ever leave for aquariums outside their native ranges.
I also believe a few aquariums are trying to keep Whale Sharks (Japan and Georgia Aquarium, possibly others).
10 Largest Aquariums in the World
As mentioned elsewhere, touropia's list is wrong. For a correct and up-to-date list see
http://www.zoochat.com/2/giant-fish-tanks-world-400917/
Whale sharks are currently kept at Geogia + aquariums in China and Japan. The elasmollet.org site is still useful for several species, but most entries haven't been updated in several years.
