In an odd twist of linguistic history, many languages have no real name for the color orange. In English, for example, the hue was know just as "red-yellow" until the orange fruit became widely available. That's not to say the color has had no part to play in history. The color is of course associated with the sixteenth century monarch, William of Orange, who helped establish the Netherlands as an independent state. In response to that history, the Dutch flag originally consisted of horizontal bands of orange, white and blue. But in the 1600s orange dyes were notoriously unstable and tended to turn red over time. Eventually the Dutch simply changed the top stripe to be red as opposed to orange but some of the colonies they established before the change still reference the original flag. New York City, for example, was established by the Dutch as New Amsterdam in 1664 and it's flag remains a variation on the original Dutch flag with vertical bands of blue, white and orange.
If orange played an important role in seventeenth century European history, it also played an important role in more recent American history as well. The Bell X-1, the first airplane to break the sound barrier, was painted international orange so as to be more visible against the blue of the sky. Space Shuttle astronauts used to wear international orange pressure suits during take-off and landing so as to be more visible in the event they had to abandon their spacecraft.
International orange can be seen throughout the built landscape as well. The color is closely associated with the aerospace industry and so you often see it near airports or tall structures that pose a danger to low-flying aircraft. The Tokyo Tower, for example is painted in alternating bands of white and international orange.
But probably the most famous structure painted international orange is the Golden Gate Bridge. There is some debate on whether it was painted this color so that it would be more visible during San Francisco's many fog events or if it was simply the color of the lead primer first used to paint it.
But whatever the reason, the Golden Gate Bridge is aesthetically striking. Its color may be based on an engineering need, but its aesthetic presence is nothing short of spectacular. If the bridge was painted any other color it would still be impressive, but it wouldn't be nowhere near as memorable. Take as an alternative the Oakland Bay Bridge which is arguably the more impressive engineering achievement but is painted a uninspired grey.
There are many things architecture has to do to in order to be good, but it has to do something more in order to be great. Sometimes it simply must be painted orange.