Of all the iconic creatures of High Fantasy the Dragon is probably the least likely.
A fearsome flying, fire-breathing, often speaking, some times spell casting, giant lizard with near unpiercable hide and a seemingly insatiable appetite for princesses.
Such a creature is so unlikely that it has become my standard response to players who insist on questioning the "realism" of a fantasy world. "You have no trouble with flying, fire-breathing dragons but you have a problem with X?"
What's wrong with dragons? Well let's start with what's right. Size, we know from dinosaurs etc that reptiles can grow to enormous size. Sleeping for years after eating, again reptiles eat infrequently and many species undergo periods of prolonged hybernation. Intelligence, well...if you have a brain as large as a dragon's, why not? Armoured hide, the Romans made armour of crocodile hide, and scales and bony plates can be quite an effective defense. Fangs and claws, just look at nature red in tooth and claw. Even the bed of gold has its parallels in jackdaws and packrats stashing away interesting and shiny trinkets. And spell casting is no problem, after all this is Fantasy and magic is de riguer.
So what about the rest?
First, flight. How do dragon's fly? Most illustrations of drgons have wings that are too small for flight, and some have wings of almost impossible anatomy. Then there is the weight of the creature. Dragons are going to be very heavy... If we give them hollow bones and internal airsacs like birds to reduce weight they can fly (maybe) but become extremely fragile. Look at the Pterosaurs that grew to enormous size, they were spindly creatures.
Second, firey breath. How on earth do you make this one work? Do dragons have respiratory tracts lined with asbestos? Terminal GERD? The most sensible explanation I have seen is highly inflamable venom that the dragon spits or sprays. Belching hydrogen gas or similar might also work. Belching hydrogen would also help with flight as those airsacs I mentioned above could be filled with it.
I do however have an answer to all the issues with dragons. It is admitedly a bit of a cop out, but... MAGIC. Dragons fly because they are magic. Same reason they breathe fire, elves have pointed ears, wizards cast spells, orcs are ugly, etc. Magic. Also known as the Walter Cronkite rationale "And that's the way it is."
I do find suspension of disbelief easier if things are kept semi-plausable, but in a fantasy world you have freedom to break the rules occasionally.
A world with realistic dragons would be a less magical place.