Mahad had the Millennium Ring before Thief King Bakura. In the present day at the start of the anime Ryo Bakura had it, he later lost it to Yami Marik. After Yugi defeated Marik, Marik Ishtar gave the Ring to Yugi. When Rex and Weevil mistakenly took Yugi's Millennium Items in an attempt to steal his Egyptian God Cards, Yami Bakura retrieved it back from them. Also, as seen in a brief scene from the manga, Mana gained the Millennium Ring after the final battle with Zorc.
Thousands of years before the events of Yu-Gi-Oh!, Alexander the Great came into possession with this item. During his time, he won many battles with it, and claims it to be his lucky charm; but, years later, the Ring somehow corrupted his mind (Possibly, it has the power split a person's soul into two pieces: one is Alexander's light-soul and the other is Alexander's dark-soul due to the fragment of Zorc's soul and his power being sealed away).
In the manga, this ring has a gruesome effect on a wearer who has not the power to maintain its shadow powers. If the wearer is not strong enough, then the ring will burn their soul and body. As seen when a thief who tried to steal it, and was forced to wear it by Shadi, after the ring's prongs punctured his chest, the thief had fire pouring out of his eyes and mouth and died horribly, a scene that Maximillion Pegasus saw, who was then subsequently forced to accept the Millennium Eye.
The strong people who managed to survive the ring's power are: Mahad, Ryo Bakura, Alexander the Great, Dark Marik, presumably, Mana in the manga, and Seto Kaiba in the Yu-Gi-Oh! Monster Capsule GB video game.
The ring is also featured on the chest of "Ma'at".
Its primary power is to guide the owner to whatever he seeks, including other Millennium Items, like a compass. It even detects non-physical objects like mystical energies or dark emotions. Like the Millennium Puzzle, it had a soul sealed inside of it, in this case a fragment of the soul of Zorc Necrophades (who had also lost his memories) and a portion of Bakura's past life, Thief King Bakura.
It also has powers of the Shadow Game. It can materialize Duel Monsters into the real world, initiate Shadow Games where the players cannot be disturbed, cast illusions, and manipulate souls. It also gives the owner dark powers, including erasing memories, remote viewing, interfering with other Millennium Items, infusing objects with a portion of the owner's spirit, and knocking people unconscious.
In the Memory World arc, it can put its owner's soul with last will into monsters like Mahad did to Illusion Magician. Bakura also used it to access his Diabound's ability to camouflage itself in the dark, so he could sneak into the Pharoah's palace.
The Ring also has an unexplained bond with its owner, as shown when Bakura mysteriously regained the Ring after Tristan threw it off a cliff into the forest in Duelist Kingdom. It could only have this effect due to Zorc's malignant powers.