So one of my favorite examples of this is that there was a lot of desire in the 1960s to set off another Little Boy test bomb, a virtual model of the first one. The reason is because while the Fat Man bomb was a design that was repeatedly tested (as the Trinity "gadget," but also in later design development), the Little Boy was a true one-off weapon. The result is that while they knew the radioactive emission spectrum of a plutonium implosion bomb fairly well, they had very little clue about the specifics of the Hiroshima bombing when it came to radioactivity. And that was a problem, because Hiroshima and Nagasaki provided all of the actual human data on prompt radioactivity exposure to actual nuclear weapons — and we still use that dataset today for setting radiation standards for all manner of things.
Norris Bradbury, the director of Los Alamos after Oppenheimer, put the kibosh on all such efforts. The Little Boy bomb was "hideously unsafe" by later standards (it had many, many critical masses of uranium in it), and it seemed like a hard thing to get anybody higher up to sign on to. (Especially after the signing of the Limited Test Ban Treaty.)
So instead they built a custom, Little Boy-shaped prompt nuclear reactor, using the front-end of a stockpile Little Boy weapon casing. From this they apparently gleaned some useful information.
Well there's only one i know of but it's pretty recent. In the 70s a bloke called Lang Hancock financed a study to test the feasibility of using atomic bombs for mining purposes in Australia as well for doing civil engineering in the form of exploding a new harbour. These got shut down for a few reasons notably people were uncomfortable with the civilian use of nuclear weaponry.
Let's not forget the nuclear rocket engine experiments at the Nevada Test Site. The infrastructure included one of the world's shortest "short line" railroads, which the workers named the "Western and Jackass Flat Railroad." It went a couple hundred yards from the rocket assembly building (where they also "cleaned" the equipment). When I visited the location in the early 1990s, there was an HO gauge model railroad still in the building, constructed by one of the workers. One of the railroad engines is now at the Nevada State Railroad Museum, Boulder City (in southern Nevada). The facility included multi-paned, lead-filled windows that were several feet thick (with mineral oil between the panes). Elaborate mechanical arms allowed workers to "handle" the equipment after each test. The engine also had heavy shielding to protect the workers who hauled the engines to and from the test platform outside the building. They tested several engines, but the idea of these engines - and sitting in a spacecraft hurled through space by a nuclear reaction - ceased to be perceived as a good idea.
One of the largest largest nuclear weapons ever constructed or detonated was the Big Ivan. (Also known as Tsar Bomba) It was originally designed to be a 100mt yield device but was later revised. The device needed to be severely limited in power partially because of concerns over nuclear fallout, but also because, the pilot and crew dropping the bomb only had a 50% survival rate; if the device had been detonated at its maximum potential, this would have almost certainly been 0%. The device did indeed have the potential to be detonated with a yield of 100 megatons, though, but after some modifications- particularly using a lead tamper instead of one made of depleted uranium in at least one of the three stages, and possibly two, this was halved to a “mere” 50 megatons, which for your reference is over 3000 times more powerful than the bomb dropped on Hiroshima.
