The One Ring granted its wearer the ability to see into and control the minds of Middle-Earth's ringbearers: the rulers of the Dwarves, the Men, and the Elves. Wearing the ring put its user halfway between the realms of light and shadow, causing him or her to become nigh-invisible in the world of the living, but plain and noticeable by the wraiths under Sauron's control. It also bolstered physical strength, though it seems that only Sauron was able to make use of this power.
The novel The Lord of the Rings involves the quest of the hobbit Frodo Baggins to destroy the One Ring. The ring was extremely durable: it was impervious to physical trauma, and could not be melted or even heated in a regular fire. The only place where the ring could be destroyed was in the lava of Mount Doom, the volcano where it was forged. It was nearly destroyed there by Prince Isildur after Sauron's defeat at the end of the War of the Last Alliance, but the ring tempted him, and he chose to keep it for himself.
Sauron poured a portion of his soul into the One Ring, an act that permanently connected him to it, and that gave the ring a life of its own. Throughout its existence, the ring adjusted its size and shape in order to be carried and lost by different bearers, including Isildur and Gollum, as it desired to return to its fallen master.
The potential of the ring made it tremendously desirable to those seeking military might, and the ring itself would play on this temptation, imposing its image on its bearer's minds and making it difficult for them to part with it. Invariably its keepers would describe it as "precious." The only character to wear the ring and then resist its lures was Samwise Gamgee, who used his "plain hobbit sense" to recognize his contentment as a gardener.