PS- the rings are named Nenya, Narya, and Vilya.
Nenya is worn by Galadriel, and is the ring of water
Vilya is worn by Elrond, and is the ring of air
Narya is worn by Gandalf, and is the ring of fire.
Remember in the Balrog standoff scene, Gandalf says "I am the servant of the secret fire, wielder of the flame of Arnor!"? he's referring to Narya, the ring he wears.
The three elven rings are in fact the "three rings for elven kings under the sky", three of the rings of power under Sauron's command. The elven rings, however, were made more powerful than any of the others save for, of course, Sauron's One Ring. Upon Sauron putting on the One Ring, he was aware of this, and likewise so were the elves of Sauron's who then removed their rings. Once Sauron was "destroyed" and the One severed from his hands, the Elves used their three rings again to help maintain their domains (Lothlorien and Rivendell). Once Sauron rose to power again, however, they knew that should he conquor that the rings would be directly under his control again, and should he fail that the power of the rings as well should fail and therefore so would their society.
The ring of Aragorn is more properly known as the Ring of Barahir, given to Barahir long ago by Finrod Felagund (one of the high elf kings) for coming to his rescue in battle.
So there you go, a little history on each ring!