A successful icon doesn't have to be functional. The Sydney Opera House, for example, didn't make structural sense, cost 10 times its original estimate, and the main hall never really worked well as an opera house (it's now used as a concert hall). Nevertheless, functional failings can sometimes sink a would-be icon. The Olympic stadium in Montreal, designed by the Parisian architect Roger Tallibert for the 1976 Games, was one-of-a-kind, with a retractable fabric roof suspended from steel cables. Since the cables were strung from a tilted, 40-story mast, the iconic ambition of the Leaning Tower of Montreal was plain. However, the roof never worked properly, and, after self-destructing in a high wind, it was replaced by a fixed cover. Although the stadium was used by the Expos, it was always an unpleasant ballpark—too dark, too much concrete, and at a billion dollars, too expensive. Montrealers, who never warmed to the stadium, called it "The Big Owe."

Correction, Aug. 11: The article originally implied that the Sydney Opera House is no longer used for opera. While the main hall is now used as a concert hall, opera is performed in a smaller stage theater.