Convair XFY-1 Pogo
Year of first flight: 1954
One of several early experiments in vertical take-off and landing (VTOL) fighter technology, the XFY-1 was designed to take off and land from a peculiar, nose-up position, turning horizontal once it had gained altitude. This would've allowed it to be mounted aboard all sorts of non-aircraft-carrier ships, giving them much-needed flexibility in the post-battleship era following WW2. That's a whole lot of hyphenated rationale just for one plane.
Ultimately, the XFY-1 turned out to be awkward to both fly and land, with the pilot essentially having to peer over his shoulder to keep the thing straight, so it never really caught on.