The Doctor's signet ring

The Doctor once owned a signet ring in which was mounted a large blue crystal. It had originally belonged to the Other. (PROSE: Cold Fusion)

The Doctor wore the ring on the middle finger of his right hand in his his first incarnation, (TV: An Unearthly Child) but soon discarded it after his regeneration into his second incarnation, as it did not fit him any longer. (TV: The Power of the Daleks)

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)

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)

After the Doctor's first regeneration, the ring no longer seemed to have any use because it no longer fit his hand. (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 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)

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