It was Elven craftsmen who first wrought the nineteen Rings, as Sauron bade, and gave to him those for the Dwarf Lords and the Men keeping the three for the Elf Lords. As a result, those three Rings were not corrupted as the others were, but their power was limited by the One that Sauron wielded. They are held now by Lord Elrond, Galadriel, and Gandalf.
The Elven contribution to Frodo's errand was the archer Legolas, a Wood Elf from Mirkwood to the North.