Well, not every Elf was like that. Some of them even fought the selfish ones, and there were a few wars with the Noldor(the arrogant ones) and the other breeds of Elves. Once Men appeared, most of them allied with the Noldor, though.
They did indirectly influence the creation of the Rings-if you've read The Lord of the Rings, it's not a spoiler to say that the Great Enemy, or Morgoth, was overthrown.
The world was made by the Ainur(angelic beings) at the direction of Eru(God. He was called Ilúvatar later). The Ainur literally sang the world into existence; their music filled the Void to make it full. However, one of the Ainur, Melkor, distorted the tune and tried to make his own-he had a desire for the power to create life himself. But the result was chaos, as the new tune clashed horribly with the original. When this continued, Eru stopped the music and proclaimed that the world was finished. He cast Melkor into the world and exiled him. He then gave the other Ainur a chance to enter the world. The downside of this was that if they did, they would become connected to the world(Arda) and would be unable to leave it until the end of time. Some of the Ainur loved Arda so much that they decided to enter it anyway, and became known as the Valar, the powers of the earth. The Valar had servants; the Maiar, who were lesser beings. Melkor waged war against the other Valar and tried to destroy the world. Because the Valar could not again enter Eru's full presence while Arda lasted, they held counsel together and decided to defeat Melkor. However, the Elves were then created, and the Valar could not wage full war with Melkor without hurting them.
Anyway, eventually Melkor/Morgoth was defeated with the help of the Noldor, and one of his Maiar, Sauron, rose to the throne. So yes, the Noldor had something to do with it.