Q:

What was the fate of Ancalagon the Black?

In The Fellowship of the Ring - The Shadow of the Past, Gandalf is discussing methods of destroying the ring, wherein he mentions this: 

It has been said that dragon-fire could melt and consume Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself.

When was Ancalagon the Black slain? I suppose it was probably at the end of the First or Second Age, but I do not recall ever reading about it.

A:

Eärendil killed him at the end of the First Age. "Of the Voyage of Eärendil and the War of Wrath" from the Silmarillion has:

Before the rising of the sun Eärendil slew Ancalagon the Black, the mightiest of the dragon-host, and cast him from the sky; and he fell upon the towers of Thangorodrim, and they were broken in his ruin.

This is during the last fight of the war (between the winged dragons on one side, and Eärendil and the Eagles on the other), right before Angband is broken open and Morgoth sues for peace.
(So Gandalf is speaking purely theoretically; Ancalagon and the One Ring never existed at the same time!)

