Well, the easiest way to look at this is what they represent in each culture. Some cultures actually vary quite widely. Take Medieval Europe, the dragon was mostly considered a beast, hoarding treasure and killing all those who trespassed. They were rarely intelligent, and even when they were they were little more then personifications of greed. They were to be slain as pests.
Now we look at China: Dragons are supremely intelligent, far more then all but the most wizened humans, and creatures to be revered. They’re giant and beautiful, and in many cases are representations of impressive natural phenomenon, like raging rivers.
So, while they’re all called ‘Dragons’, it’s rather hard to classify them together. In general it’s probably related to their ‘badassness’, as kvlt said. No matter what, they are depicted as being incredibly powerful. Be it that they’re intelligent or beasts, they’re always things of awe. Capable of flight, breathing fire (which has always been a horribly powerful destructive force), and far stronger then any man: they’re formidable. So, we use them as idols, so to speak, of power, be that power of blind destruction or intelligent construction.