First, we cannot regard traditions about dragons as being worldwide. Because of issues with translation, the English language word "dragon" is used for a wide variety of unrelated creatures found in international folklore. The use of the term indicates some similarities, but closer examination demonstrates that the entities are very different and that they are unrelated both historically and by core characteristics.

With that out of the way, the European dragon was regarded as a dangerous creature that was generally thought to exist in a remote past or in a remote place. People believed they had existed or they existed a long way off; people did not generally report encountering dragons in the way that they told legends of encounters with ghosts or fairies, for example. Beliefs in these remote dragons persisted into pre-modern times. I don't know if anyone has conducted a survey to see if people continue to believe that dragons existed in a remote time or place, but I suspect that for some, the belief persists.

The Asian dragon is an entirely different creature. It is generally believed to be associated with good fortune. Many cultures conceive of this creature as being capable of invisibility, and because of this, it is easy to imagine the entities as still existing. It is my understanding that belief persists.

These are only two examples of traditions associated with large creatures that more or less have dragon-like attributes. The answers to your question when considering various international traditions would depend on the folklore of each culture - and how each has changed over time.

I'd like to add to /u/itsallfolklore's excellent answer, echoing that medieval Europeans generally thought of dragons as real creatures that lived somewhere "out there," either in sub-Saharan Africa or East Asia.

That said, you might be interesting in a peculiar passage from Roger Bacon's Opus Majus (1266 CE), a sprawling synthesis of medieval science:

“It is certain that Ethiopian wise men have come to Italy, Spain, France, England, and to those lands of the Christians where there are good flying dragons. Through a secret method that they possess, they lure the dragons from their caves, have saddles and bridles at the ready, mount them, and ride them, bravely flying through the air so that the stiffness of their bodies is eased and their hardness tempered — just as boars, bears, and bulls are driven by dogs and whipped with various beatings before being killed for food. When they have thus tamed them, they have a way of preparing their meat just like the way of preparing Tyrian [snake] meat. The meat is used against the accidents of old age; it prolongs life and sharpens intellect beyond all estimation. No man-made teaching will lead to as much wisdom as eating their meat, according to what we have learned from men of proven trust, without falsehood or doubt "(Opus Majus XII.II, my translation).

So, to review: Roger Bacon, an English friar and university-trained philosopher, writing for the Pope, was comfortable asserting that African dragon hunters traveled to western Europe and other "Christian lands" to capture, ride, kill, and eat cave-dwelling, flying dragons. While dragons (and their apparently life-changing meat) are not here treated as something commonplace, it's remarkable to be reminded that the European dragon lore was not just a peasant superstition or an exotic rumor about distant places. Dragons might be found -- and ridden, apparently -- much closer to home.