Sorry, had to throw this in since I saw Glaurung mentioned...while he is the most important, and Smaug awesome...there was one greater than both!
Ancalagon the Black
Ancalagon: (Sindarin: rushing jaws from anc 'jaw', alag 'impetuous'[2])
Morgoth bred Ancalagon during the First Age to be the greatest and mightiest of all dragons, and the first of the winged ‘fire-drakes’. He arose from the inferno pits of Angband like a storm of wind and fire as a last defence of the realm of Dor Daedeloth. Near the end of the War of Wrath that pitted Morgoth’s hosts against the Host of the Valar, Morgoth sent Ancalagon leading a fleet of winged dragons from the fortress of Angband to destroy the Dark Lord’s enemies. So powerful was the assault of the dragon flight that the Host of the Valar was driven back from the gates of Angband onto the ashy plain of Anfauglith.
From the west, Eärendil 'The Blessed' in his powerfully hallowed Elven airborne ship Vingilot, aided by Thorondor and the great Eagles, dueled with Ancalagon and the dragon fleet for an entire day. At length Eärendil prevailed, casting Ancalagon upon the triple-peaked towers of Thangorodrim and destroying both dragon and towers. With his last and mightiest defender slain, Morgoth was soon utterly defeated and made captive, ending the War of Wrath.
Ancalagon the Black is considered to have been the greatest dragon of Middle-earth, undoubtedly the largest, and is often referred to as the ‘father of the winged-drakes’. He was so large his body was able to crush the volcanic Thangorodrim, the highest peaks in Beleriand. Like all other Urulóki, Ancalagon breathed fire, which was said to be hotter than any other known flame.