The more powerful of the two fundamental divisions of dragon-kind, who, as the name suggests, were able to breathe fire. Glaurung, Ancalagon and Smaug were all fire-drakes. The only explicit reference is in The Silmarillion (Of the Return of the Noldor); "…Glaurung, the first of the Urulóki, the fire-drakes of the North, issued from Angband's gates by night."
Smaug, the last of the truly powerful dragons, was slain by Bard in the late Third Age. We can be sure that he was not the last of the fire-drakes, though, because Gandalf refers to fire-breathing dragons in the time before the War of the Ring, nearly eighty years after Smaug's death. Tolkien even goes so far as to hint that some of these creatures might have survived to our own times.