[bilbo_baggins]

Well to embody the replies:

Tom Bombadil is another Ainur (definition of Ainur being a creation of Eru) and he is the oldest (I got this from burrahobbit's post). But not the oldest Non-Valar/Maiar.

Ents and Elves are equal in age, for the Entian spirits were sent to inhabit the special tree carriers and awaken at the time of Awakening (Elvish awakening) and they later learned to speak from the Elves. Learning to speak does not mean they were less mature than the Elves. Is it not said that the Wise hold their tongue, while the foolish speak their folly plainly?

The Dwarves had a preawakening existence, for they cringed at the impending destruction by Aule's hammer. So technically, they are older than the Elves. But were the Entian spirits alive before they were sent to inhabit trees? That's the question; and it boils down to:

Tom Bombadil is older than anything else on Arda, because he IS Ea. Dwarves sorta/kinda outage Elves, but not really. Elves and Ents awaken at the same time and are equal in power. Ungoliant is a Maia, I believe (I can't know for sure).

So if you like to pick nits, "Go Dwarves!"

If you hate technicalities, "Go Elves!" (Ents are sort of like ethereal spirits and come from Eru directly, not like the Elves)