As recalled by Bernice Summerfield, the Seventh Doctor spoke with a Scottish accent, specifically of the Highlands. (PROSE: Big Bang Generation) Through the TARDIS' telepathic circuits, Elizabeth Klein heard the Seventh Doctor speaking German in "a stuffy Prussian accent". (AUDIO: Survival of the Fittest)
The Master inherited the American accent of Bruce when he possessed his body. (TV: Doctor Who) Whilst exploring the Eighth Doctor's TARDIS, River Song thought she heard an American screaming from within the walls. (GAME: The Eternity Clock)
The Ninth Doctor was often questioned about his Northern accent, since he was not human. (TV: Rose, et al.) He would often retort "lots of planets have a North." (TV: Rose, The Parting of the Ways) The Eighth (TV: Doctor Who, et al.) and Thirteenth Doctors (TV: The Woman Who Fell to Earth, et al.) also exhibited Northern accents.
The Twelfth Doctor initially thought everyone else had changed accents (when in reality, he did), due to his post-regeneration delirium. But he soon took his Scottish accent as an entitlement to complain about things. (TV: Deep Breath) He could imitate an American accent. (TV: The Zygon Inversion)
Rose Tyler naturally spoke in an accent characterised by Chip as "old Earth style cockney", which the Lady Cassandra, while possessing her body, made a poor imitation of while posing as Rose to the Doctor. (TV: New Earth) Elton Pope deduced that Rose was "definitely" from London by her accent. (TV: Love & Monsters) Rose herself briefly imitated a Scottish accent while in Scotland of 1879 until the Doctor advised her not to. (TV: Tooth and Claw)
Jack Harkness, likely due to the centuries he lived, was able to change his accent as he wished. He demonstrated being able to imitate a Texan accent, (TV: Greeks Bearing Gifts) a Welsh accent, (TV: Dead Man Walking) and an English accent. (TV: End of the Road) While acting as the seventh incarnation of the Doctor, Jack adopted the Sixth Doctor's accent. In turn, the Sixth Doctor adopted Jack's accent when he pretended to be him. (AUDIO: Piece of Mind)
The TARDIS translation circuit often had people confused about where the time travellers were from. In Pompeii in August 79, both the Tenth Doctor and Donna Noble spoke Latin when their speech was already being translated into Latin; it came out sounding Celtic. (TV: The Fires of Pompeii) When Amy Pond met Vincent Van Gogh, her speech was translated into French; however, due to her Scottish accent, Vincent thought she was from Holland. (TV: Vincent and the Doctor)