The Aircraft Nuclear Propulsion Program. Ran for fifteen years and about a billion dollars back when that was real money. I'm deluded enough to believe that a nuclear-powered airplane could actually maybe be a good idea, given various assumptions about radiation health effects I won't get into here. But, even if you agree that an atomic-powered plane could be worth having, ANP was too badly mismanaged to produce a viable aircraft. Here's why:
First, while the actual project leaders such as Gen. Keirn seem to have been competent and effective, the higher-ups could never decide if they really wanted the thing. This was the story from the very beginning of the project in the 40s - once NEPA, the ANP's predecessor, finished its feasibility study, the AEC asked the Joint Chiefs if they wanted to set up a joint development program. It took two years for the JCS to respond, and when they did they said they wanted it tomorrow. This pattern continued through the whole history of the program; they alternated between crash projects to build an A-plane yesterday, and leisurely materials development that would consider making something in the 70s. One engineer I spoke to described it as "hire on even years, fire on odd."
Second, the project was jointly funded by the AEC and the USAF - and, instead of setting up a single contracting authority, each agency signed separate contracts with the developers. Which naturally led to the developers playing the USAF and the AEC against each other, to the extent it took two years from the signing of the letter of intent to when Pratt & Whitney actually started working. (This problem was eventually fixed, but not until too late in the day to save things).
Third, development was focused on the direct-cycle turbojet design, in which air would be passed directly through the reactor. This was in contrast to the indirect-cycle, where a coolant such as liquid metals or pressurized helium would run between the reactor and a heat exchanger in the turbojet. The direct cycle had the advantage of simplicity and... Well, that was about it. Indirect cycle engines promised greater safety and much better performance, since the poor thermal properties of air would make your reactor much, much bigger than it could be using a better coolant. An indirect-cycle engine could potentially be worth using; it could maybe even be good enough to power a combat aircraft. A direct-cycle engine would be a technology demonstrator with limited applicability to further development.
Fourth, the Air Force was only interested in nuclear propulsion if it was propelling a supersonic bomber. The technical challenges of nuclear propulsion were prohibitive as it was, demanding supersonic performance using a direct-cycle engine made it almost impossible. ANP tried to get around this by adding chemical-fuel afterburners and only going supersonic over the target, and ended up designing a plane that would weigh more than half a million pounds, cost a fortune, and still be worse than a conventional jet bomber.
Fifth, the whole crashing issue. 'nough said.
By the time Kennedy was inaugurated, even most of the project's adherents thought it was time for it to go. Kennedy and MacNamara finally put it out of its misery in 1961.