Tenth Doctor's coat

The Tenth Doctor wore a double-breasted Duster-type overcoat of cinnamon brown Alcantara as part of the costume he chose in the TARDIS wardrobe following his regeneration from the Ninth Doctor (TV: The Christmas Invasion) He claimed that the coat had been given to him by Janis Joplin. (TV: Gridlock)

The Doctor would typically throw the coat off in preparation to flying the TARDIS, (TV: New Earth, Army of Ghosts, Smith and Jones, Human Nature, The Unicorn and the Wasp, The Stolen Earth, The End of Time) upon entering a property, (TV: The Girl in the Fireplace, Fear Her, Evolution of the Daleks, The Sound of Drums, The Sontaran Stratagem, The Doctor's Daughter) or when about to do something of which the coat would get in the way. (TV: Gridlock, Evolution of the Daleks, Utopia, Silence in the Library)

Before regenerating into the Eleventh Doctor, the Doctor threw the coat aside in the TARDIS control room. (TV: The End of Time)

Others
The Fourteenth Doctor, who bore a curious resemblance to the Tenth Doctor, emerged from his regeneration wearing a similar overcoat of navy blue tweed. (TV: The Power of the Doctor)