Gaunt's Ring was an heirloom of the Gaunt family, descendants of Salazar Slytherin and Cadmus Peverell. It is a gold ring inset with a black stone engraved with what Marvolo Gaunt called the Peverell coat of arms (having come into the Gaunt line from an heiress of the Peverells, not the Slytherin family). The signet ring passed through the male Gaunts, generation to generation, until it was stolen from Morfin Gaunt by Tom Riddle while Tom framed Morfin for the murders of the Riddles.
While at Hogwarts, Tom openly wore the ring. He later used the ring, as an heirloom of the Gaunt family, as one of his Horcruxes. Tom did not enchant the ring right away, as he was seen wearing it while asking Horace Slughorn about horcruxes, as seen through Slughorn's memories through a pensieve.
Powers
Being a Horcrux placed the ring under a curse. Unknown to either the Gaunts or Riddle, however, the stone in it was the Resurrection Stone, one of the Deathly Hallows.
History
The ring's story begins (and ironically ends) with its black stone. The stone happened to be the Ressurection Stone, one of the Deathly Hallows of legend, and had the symbol of the Deathly Hallows engraved on its surface. According to the Tale of the Three Brothers, Cadmus Peverell, the middle brother, asked Death for the power to return people from the dead. Death supposedly picked up a black stone from the nearby river bank and gave it to Cadmus, promising him that it contained the power he had requested. Once Cadmus returned to his home, he took out the Resurrection Stone and turned it over in his hand three times. In doing so, he brought back his lover who had suffered an untimely death. While she did return from the dead, she was not truly alive and wished to go back to the world of the dead since she no longer belonged in the living world. For Cadmus, it was like being able to see her but not able to touch her or truly be with her. Seeing the stone's limitations drove Cadmus to madness, and he took his own life to truly join his love in death.
The stone passed down Cadmus' family line. At some point, it was placed into a gold setting and made into a ring. The ring continued to be passed down the family line, eventually ending up in the hands of the Gaunts. Marvolo Gaunt, the family's patriarch at the time, prized this ring (along with Salazar Slytherin's Locket) more than anything (even his own children). When the family was visited by Ministry of Magic official Bob Ogden, Marvolo waved the ring in front of his face in an attempt to impress and intimidate Ogden. When Marvolo and his son Morfin Gaunt were arrested and imprisoned for assaulting Muggles and Ministry officials, his daughter Merope Gaunt abandoned the family to escape the mental torture her father continuously employed against her, taking Salazar Slytherin's Locket with her. When Marvolo returned home, he had expected to find his daughter dutifully awaiting his return. What he found however was a house covered with an inch of dust and a note from Merope explaining what she had done and why. Marvolo died shortly thereafter, either due to his inability to take care of himself or the weakening of his strength from Azkaban. The signet ring passed to Morfin when he was finally released from Azkaban, and he continued to wear it in his delusional state for several years afterward.
Some years later, Tom Marvolo Riddle returned to Little Hangleton to seek out his family. He had been expecting to meet Marvolo, but instead found the half-crazed Morfin in the Gaunt Shack. Morfin remarked how Riddle looked very much like the muggle that had married his sister, Tom Riddle Sr.. He told Riddle how Riddle Sr. had abandoned Merope and returned to his parents' home, the Riddle House. Upon learning of his father's abandonment (and thus feeling that he had caused Merope's death), Riddle stunned Morfin and took his wand. He then proceeded to the Riddle House to confront his father. Frank Bryce, the Riddle's gardener, remarked later that he had seen Riddle ascending the hill toward the house. Riddle used a common spell to unlock the door and entered the house. Once inside, Riddle found his father, along with his parents Thomas Riddle and Mary Riddle, in the drawing room. Riddle then used the Avada Kedavra Killing Curse on his father and muggle grandparents. It is unknown if there were any words exchanged between them before the actual murders took place, but what is certain is that the Riddles were found dead in their drawing room. Riddle returned to the Gaunt Shack and modified Morfin's memory to make him believe that he had killed the Riddles himself. Riddle replaced Morfin's wand on his person but absconded with the ring. When Morfin was arrested by the Ministry and found guilty of the Riddle murders, he was carted off to Azkaban for good this time. As he was being taken away, he continously remarked that his father would kill him for losing the ring.
Riddle openly wore the ring at Hogwarts after these events, as seen on his hand in a memory provided by Potions Master Horace Slughorn. Riddle then questioned Slughorn about Horcruxes, particularly what would happen to the wizard that created more than one. By this point, Riddle had already created his first Horcrux, his childhood diary, with the murder of a fellow student named Myrtle. At some point shortly before or after his graduation from Hogwarts, Riddle used the murder of his father, Tom Riddle Sr. to turn the ring into a Horcrux. He then chose to return it to the very place he had stolen it from: the Gaunt Shack. He placed the ring inside a golden box and hid it beneath the shack's rotting floorboards. He then set up many protective enchantments to deter outsiders from entering the shack and finding the ring. He also placed a powerful curse on the ring as well, one that would quickly lead to the death of the ring's wearer if not stemmed. The ring was left there in the ruin of the Gaunt Shack for many decades to come.
In 1996, Albus Dumbledore began investigating Riddle's obsession with immortality and his fascination with Horcruxes. Dumbledore suspected that a good place to look for one of Riddle's Horcruxes would be the Gaunt Shack, considering its importance to Riddle's past. Dumbledore traveled to Little Hangleton and found the remains of the shack, hidden amongst many weeds and brush. Dumbledore succeeded in passing through the enchantments protecting the shack and discovered the golden box holding the ring beneath the shack's floorboards. He brought the sword of Godric Gryffindor with him as it now had the power to destroy Horcruxes since Harry had used it to kill the Basilisk of the Chamber of Secrets, which imbibed the blade with the Basilisk's venom. However, Dumbledore recognized the symbol of the Deathly Hallows on the ring's black stone and recognized it as the Ressurection Stone, something for which Dumbledore had searched for the greater part of his life. Hoping to revive his dead family members (particularly his sister Ariana Dumbledore), he disregarded the ring's status as a Horcrux and put it on. This enacted the ring's deadly curse, and it began to quickly spread through Dumbledore's body, starting with the hand on which he had put the ring. Dumbledore got the ring off and used Godric Gryffindor's sword to crack the Resurrection Stone, believing this might stop the curse from spreading. While the act did disarm ring as one of Riddle's Horcruxes, it did not stop the curse that was now quickly killing Dumbledore. He took the ring and quickly returned to Hogwarts, where Severus Snape intervened and was able to stem the curse (confining it to Dumbledore's hand), but only temporarily. Snape gave Dumbledore a prognosis of about a year, and told him the curse would eventually bring upon him a very painful and humiliating death. It was then that Dumbledore asked Snape to kill him when the right time came to spare him the painful death the curse would exact upon him otherwise. After some persuasion, Snape agreed to the plan (which was enacted at the climax of the First Battle of Hogwarts atop the Astronomy Tower).
Before his death at Snape's hands, Dumbledore magically sealed the cracked Resurrection Stone inside the very snitch Harry had caught at his first ever Quidditch match. The snitch would only open and yield the Ressurection Stone to Harry when he was about to "die" (the snitch read "I open at the close"). After Dumbledore's death, Rufus Scrimgeour delivered the snitch to Harry, along with other possessions left to Ron Weasley and Hermione Granger. During his quest for the Horcruxes, Harry riddled over the snitch, until he finally solved its mystery at the Second Battle of Hogwarts. As Harry was about to be "killed" by Voldemort, he whipered "I am about to die" to the snitch, and it opened. Harry then used the Ressurection Stone of Cadmus Peverell to bring back the spirits of James Potter I, Lily Potter I, Sirius Black, and Remus Lupin. Their spirits comforted Harry as he walked toward his supposed doom. Upon reaching Voldemort's camp in the Forbidden Forest, Harry intentionally dropped the Ressurection Stone near Aragog's lair so as to prevent another from ever uniting the Deathly Hallows ever again. After Voldemort's defeat at Harry's hands, Harry told Dumbledore's portrait that the stone was lost in the Forbidden Forest and that he would not go look for it, a plan that Dumbledore applauded. According to Rowling, the Ressurection Stone was pressed into the earth by the hoof of a centaur, ensuring that it would never again be found.