in the Hobbit there is Smaug, of course
in the Lord of the Rings there are no dragons.
they are mentioned of course. Smaug is mentioned, when Bilbo's adventures are remembered.
also, there are 2 dragons named when recounting parts of the Hisotry of Middle Earth: Ancalagon and Scatha.
see here: http://www.cdrlabs.com/phpBB/viewtopic. ... 6949#76949
the creatures in The Lord of The Ring are not dragons. these are the "winged steeds" of the black riders.
here's the most descriptive paragraph about them:
The Return of the King, Book V, Chapter 6, page 115.
The great shadow descended like a falling cloud. And behold! it was a winged creature: if bird, then greater than all other birds, and it was naked, and neither quill nor feather did it bear, and its vast pinions were as webs of hide between horned fingers; and it stank. A creature of an older world maybe it was, whose kind, lingering in fortgotten mountains cold beneath the Moon, outstayed their day, and in hideous eyrie bred this last untimely brood, apt to evil. And the Dark Lord took it, and nursed it with fell meats, until it grew beyond the measure of all other things that fly; and he gave it to his servant to be his steed. Down, down it came, and then, folding its fingered webs, it gave a croaking cry, and settled upon the body of Snowmane, diggin in its claws, stooping its loned naked neck.
they're referred to in few ways: Winged Terror, Winged Shadow, Winged Messenger. but these references are more to the Nazgul than to their "steeds". i'm sure they don't have their own proper name.
a few more quotes:
The Fellowship of The Ring, Book II, Chapter 9, page 403.
... a dark shape, like a cloud and yet not a cload, for it moved far more swiftly, came out of the blackness in the South, and sped toward the Company, blotting out all light as it approached. Soon it appeard as a great winged creature, blacker than the pits in the night.
Almost above him the winged shaped swerved. There was a harsh croaking scream, as it fell out of the air, vanishing down into the gloom of the eastern shore.
(Legolas shoots the winged messenger)
The Two Towers, Book III, Chapter 5, page 101.
'...For he was a Nazgul, one fo the Nine, who ride now upon winged steeds. ...'
(Gandalf describing the Winged Messenger Legolas shot at at Sarn Gebir)
The Two Towers, Book III, Chapter 11, page 201.
A vast winged shaped passsed over the moon like a black cloud. It wheeled and went north, flying at a speed greater than any wind of Middle-earth.
(the Nazgul flying to Isengard after its fall)
The Two Towers, Book III, Chapter 11, page 204.
'...I heard you shout "messenger of Mordor". What was it? What could it do at Isengard?'
'It as a Black Rider on wings, a Nazgul,' said Gandalf
(Gandalf explaining to Pippin)