Elrond's ring is called Vilya, the Ring of Air. Originally crafted by Celebrimor, and passed to Gil-Galad, who fell at the Last Alliance battle. Elrond possessed the ring after that.
Gandalf's is the Red Ring of Fire, Narya. It was originally worn by Círdan the Shipwright, but he passed it on to Gandalf.
Galadriel's ring is Nenya, the Ring of Water (or also known as the Ring of Adamant).
Those three rings were made outside the will of Sauron, hence the reason he has no control over them. They allow the bearers to gain insight to the other bearer's thoughts and mind.