We know for certain (from Gandalf) that Treebeard the Ent is the oldest living creature on Middle Earth:
"Treebeard is Fangorn, the guardian of the forest; he is the oldest of the Ents, the oldest living thing that still walks beneath the Sun upon this Middle-Earth."
TLOTR Book 3, Chapter 5: The White Rider
"Treebeard is Fangorn, and the eldest and chief of the Ents, and when you speak with him you will hear the speech of the oldest of all living things."
TLOTR Book 3, Chapter 8: The Road to Isengard
But just how old is he? Obviously somewhere in the thousands of years, but I'm really curious to know exactly how old the oldest (and probably wisest) living creature in Middle-Earth is. Ent eyes are very deep, and Treebeard's eyes the deepest of all. How long have they seen?