Well,
I haven't encountered any giant talking eagles....
But let's see.
The decline of the Ents was foretold by Treebeard himself. Due the loss of the Entwives, there were no more Entings, and over time the Ents would either be destroyed by some accident involving fire, or simply grow "treeish".
The Eagles were a means Manwë the Elder King had of keeping an eye on things in Middle-earth, along with helping those who did good. I do think that as Men grew more and more numerous, they would have been recalled to Valinor, as a measure of their own protection.
As for vampires and werewolves, there was no specific mention of them after the First Age, but that doesn't mean creatures of that sort or similar weren't wandering around somewhere. They just weren't enough of them to have any sort of impact on the histories by that point.