[dancing spawn of ungoliant]

Yavanna was worried about Aulë's dwarfs and had a conversation with Manwë who said that there will be tree herders walking in the forests. Before it Manwe said that Eru had spoken to him and he had said that when the Children of Ilúvatar awake, so awakes Yavanna's thought as well and it calls spirits from far and they go in the midst of kelvar and olvar.

So it would seem that the ents actually aren't ordinary "mortal trees" but spirits living inside some things among olvar, as also hinted in the letter which Tuor referred.

In LotR (I can't remember the exact ch.) Treebeard says that some trees are getting sleepy and more tree-ish. My personal opinion is that when an ent became treeish enough he/she became a regular tree and then lived a tree's life and died like trees do.

But then there's the question about the "bad" ents/trees (Old Man Willow...). What could have made the lofty spirits turn evil? But that doesn't probably belong in this thread.