The Fairey Rotodyne, Saunders Roe Princess and the TSR2 were the stuff of dreams and endless fascination when I was young. They were about the most exiting things around and "The Future" according to "Look and Learn", "Ranger" and other publications. Later Concorde entered my consciousness, then became reality, unlike the Rotodyne and Princess. Those three did fly.
The Tarrant Tabor most certainly did not, and is thus a fine contender if you literally follow the title of this thread.
Another fine contender is the Piasecki Helistat, though it did just manage to crawl briefly into the air before disintegrating!