...`Did you not hear me, Glóin?' said Elrond. `The Three were not made by Sauron, nor did he ever touch them. But of them it is not permitted to speak. So much only in this hour of doubt I may now say. They are not idle. But they were not made as weapons of war or conquest: that is not their power. Those who made them did not desire strength or domination or hoarded wealth, but understanding, making, and healing, to preserve all things unstained. These things the Elves of Middle-earth have in some measure gained, though with sorrow. But all that has been wrought by those who wield the Three will turn to their undoing, and their minds and hearts will become revealed to Sauron, if he regains the One. It would be better if the Three had never been. That is his purpose.'`But what then would happen, if the Ruling Ring were destroyed as you counsel?' asked Glóin.
'We know not for certain,' answered Elrond sadly. `Some hope that the Three Rings, which Sauron has never touched, would then become free, and their rulers might heal the hurts of the world that he has wrought. But maybe when the One has gone, the Three will fail, and many fair things will fade and be forgotten. That is my belief.'
`Yet all the Elves are willing to endure this chance,' said Glorfindel 'if by it the power of Sauron may be broken, and the fear of his dominion be taken away for ever.'
Galadriel's ring, of course, he tells us about in the course of the story. But why do you suppose he hid Elrond's and Gandalf's rings until the end of the story? I guess when I learned about Galadriel's, I assumed that Elrond had one, mostly because he and Galadriel both seem to have the same powers to protect their enchanted little Oases, and Rivendell was obviously such a powerfully enchanted place.
How did Gandalf get his ring? - Why does a Wizard have an elf-ring? - who was intended the bearer of it, and how did that happen? - Have you told us before?