Ancalagon the Black was the mightiest of Morgoth*'s winged dragons, who fought Eärendil (and the Eagles) in the skies for twenty-four hours, eventually perishing and falling atop the mountains of Thangorodrim, destroying them.
*Morgoth was the first Dark Lord, Sauron's master
Glaurung was the first dragon, and one of the greatest. He wrought destruction and ravaged the forces of good.
Besides Smaug, the other named dragon was Scatha, who lived in the Ered Mithrin. He was eventually slain by Fram, an ancestor of Eorl the Young, and his hoard was sought by both the Rohirrim and the Dwarves of that region. The horn that Éowyn gave Merry came from Scatha's hoard.
One last note: while Smaug was the last of the truly powerful dragons, he was not the last of the Urulóki (Fire-dragons). The lesser ones survived long after his death.