Supermarine Type 300
There are plenty of examples, but if you want a classic then perhaps the Supermarine Type 300 fits the bill. It began as a cleaned-up Type 224 but, as first presented to the Air Ministry, retained the Rolls-Royce engine with evaporative steam cooling and a straight, tapered wing with room for around four machine guns.
While it was still on the drawing-board the PV12 engine moved to glycol cooling and "Merlin" monicker, the Ministry requirement to eight guns and the wing to thinner profile and elliptical planform. Yeah, the Spitfire.
That famous D-section main wing box is in fact the legacy of the evaporative cooling system.
De Havilland DH 106
The world's first jetliner is pretty classic too. When de Havilland started work on a revolutionary idea of a jet-powered airliner, they turned to the German secrets being brought back from the aftermath of war. The airliner was to have a tailless swept wing. They built a quarter-scale aerodynamic test plane, the DH 108. It was fast all right, but it came at a time when nobody understood the sound barrier and all three examples shook to bits, killing their pilots. In part that gave the shape an undeserved bad name, but mainly DH realised that it did not have sufficient trim tolerance of varying CG position during commercial operations, and a tail would fix that. Enter the DH 106 Comet, the world's first commercial jetliner.
Convair F-102/106
Here's another almost as classic. When Convair first flew the prototype delta-winged jet interceptor the YF-102, it sucked. It handled like a pig on the approach and couldn't even go supersonic in level flight. Two new discoveries at that moment included area-ruling and conical leading-edge camber. Both were applied in somewhat ad hoc and hurried fashion to the YF-102A and it made Mach 1.25 in level flight, while also being a lot tamer on the landing flight path. Time for a breather and a proper job with 50% more thrust to boot, and the F-102B, renamed as the F-106A, happily hit M 2.3.
Fairey Rotodyne
And one more for luck. In the 1950s Fairey Aviation developed the Rotodyne, a VTOL feederliner with conventional wing and propellers but also a tipjet-driven rotor. Complicated and expensive yes, but what ended the project was the noise made by the prototype - its tipjets sounded like a thousand banshees coming in for the kill.