The Doctor's signet ring

The Doctor once owned a signet ring in which was mounted a large blue crystal. The Doctor wore the ring on the middle finger of his right hand in his first incarnation. (TV: An Unearthly Child)

History
The ring had originally belonged to Patience's husband. (PROSE: Cold Fusion)

The ring played a role in the Doctor's escape from Gallifrey, which involved the breeching of "laws and barriers." (PROSE: The Three Paths)

The First Doctor was forced to sell his ring in exchange for French Revolution-style clothes when he arrived in Paris on 25 July, but had it returned to him the next day. (TV: The Reign of Terror)

He discarded it after his regeneration into his second incarnation, as it did not fit him any longer. (TV: The Power of the Daleks) Eventually, the Doctor became more reliant on his sonic screwdriver. (TV: Fury from the Deep)

It was discovered to have fallen into the TARDIS console following the Doctor's first regeneration, where it remained until it was recovered by his seventh incarnation who, having tried it on, decided to start wearing it again. (COMIC: The Chameleon Factor)

After wearing it through numerous adventures, (COMIC: The Good Soldier, Metamorphosis, PROSE: Tragedy Day) the Doctor gave the ring to Joan Redfern after he turned back from being John Smith. (PROSE: Human Nature)

Despite this, the Doctor wore the ring in his Muldwych incarnation. (PROSE: Birthright)

Abilities
The ring had several special abilities. It could supply power to the TARDIS's main doors and control a Zarbi. (TV: The Web Planet) If given the correct spectrum of light, it could unjam a TARDIS's locking mechanism. (TV: The Daleks' Master Plan) The ring seemed to be able to facilitate hypnotism and protect the Doctor from electrical shocks. (TV: The War Machines) On the Ethereal homeworld, the Doctor used the ring to open an electronic lock. (PROSE: The Cloud Exiles) When the Doctor received lessons in the "magic" of Avalon from Kilvenny Odoyle, the ring served as his "wand" through which he focused his spells. (PROSE: The Sorcerer's Apprentice) On Hogsumm, the Doctor used the ring to temporarily repair the damage bubbleshake had caused to Bernice Summerfield's mind. He later used it as a substitute operator's key for a transmat system. (PROSE: The Highest Science)

Behind the scenes
The ring plays an important part in Doctor Who: Legacy's Sonic Adventure storyline. In it, the Master steals all of the sonic devices onboard the TARDIS and scatters them through time. The ring was not stolen because it contained no sonic technology, but the First Doctor could still use it like the other Doctors used their screwdrivers and used it to get back all the sonic devices.