Elder Wand

The Elder Wand is one of the Deathly Hallows. According to legend, whoever unites it with the Resurrection Stone and the Cloak of Invisibility will be the master of death. It is the most powerful wand that has ever existed, and is able to repair other wands and allow them to function normally, something that was believed impossible at the time, as although wands could be repaired, they would have severly reduced magical power.

Creation
The Elder Wand was either made by the eldest of the three Peverell brothers, Antioch, or, according to legend, acquired by him from Death. With a core of Thestral tail hair, it is enchanted so that whoever owns it will always win a duel.

History
After killing a rival wizard in a duel shortly after obtaining the wand, Antioch drunkenly boasted of the wand's powers. He was murdered in his sleep that night, and another wizard took possession of the wand. Over time, the powerful wand passed through various owners, usually in violent circumstances, and acquired names such as "The Deathstick" and the "Wand of Destiny."

It eventually ended up in the ownership of the wandmaker Gregorovitch, who was trying to duplicate its powers. It was stolen from him by the Dark Wizard Gellert Grindelwald, who used it to cause havoc in Europe until he was defeated by Albus Dumbledore. The ownership of the wand then passed to him. Many years later, Severus Snape killed Dumbledore, who requested that Snape kill him to save him from a more agonising death, and because this act was agreed on, Dumbledore would not be 'defeated', so the powers of the elder wand would be nullified. This led Voldemort to believe ownership of the wand was Snape's.

However, Harry Potter deduced that the true owner was in fact Draco Malfoy -- before Dumbledore died, Malfoy had disarmed him and unknowingly won possession of the wand. Nearly a year later, Harry disarmed Draco and unknowingly became the wand's master.

When Voldemort used the Elder Wand to perform the Killing Curse on Harry, the wand refused to harm its true master, and instead the curse rebounded on Voldemort, finally killing him. Harry, now the true Master and owner of the wand, used it to repair his first wand. He then returned it to Dumbledore's tomb.

If Harry dies naturally, then the power of the Elder Wand, whose master would not have been defeated in battle, will then be nullified.

Other elder wands
While "The Elder Wand" (capitalized) refers to one third of The Deathly Hallows, other wands have been made from elder wood. In general wizards seem to eschew elder wands (due at least in part to the sordid history of the Elder Wand itself), favoring wands made from various other woods, such as holly (Harry), or willow (Lily Evans and Ron). Ron repeats an old wizarding saying, "Wand of elder, never prosper" after Hermione reads The Tale of the Three Brothers, to illustrate how wizarding lore may be passed from generation to generation.