Doppelgänger

Doppelgängers were individuals who were identical to other individuals. According to the Second Doctor, the idea of a doppelgänger could be found in folklore and myth across almost every civilisation. It was suggested that if two doppelgängers met, one of them would die. (AUDIO: The Night Witches)

Coincidental doppelgängers
Ian Chesterton and Robin Hood happened to look alike, (PROSE: The Thief of Sherwood) as did Polly Wright and Maid Marian, (PROSE: The Thief of Sherwood, That Time I Nearly Destroyed the World Whilst Looking for a Dress) and Tatiana Kregki, (AUDIO: The Night Witches) Strella and Romana I, (TV: The Androids of Tara) Ann Talbot and Nyssa, (TV: Black Orchid) Peri and Queen Anne (although Queen Anne had a crooked nose), (AUDIO: The Church and the Crown) William Pike and his great-grandson Darius Pike, (TV: The Cambridge Spy) Barker and his great-grandson Thorne, (TV: The Cambridge Spy) Gwyneth and Gwen Cooper, potentially due to spatial genetic multiplicity, (TV: Journey's End) cousins Adeola Oshodi and Martha Jones, (TV: Smith and Jones) and a Soothsayer and Amy Pond, (TV: The Fires of Pompeii)

The Doctor's doppelgängers
The Doctor had various doppelgängers across their regenerations. The First Doctor resembled the Abbot of Amboise (TV: The Massacre) and Solomon the trader. (TV: Dinosaurs on a Spaceship, Twice Upon a Time) Cardinal Robert Bellarmine also closely resembled him to the point of being mistaken for him by those unfamiliar with the Doctor. (PROSE: The Empire of Glass)

He also resembled Ramón Salamander in his second incarnation, (TV: The Enemy of the World) Premier Lutz in his third, (PROSE: Talons of Terror) Father Gregory in his fourth, (AUDIO: Tsar Wars) Andrew Edwardson in his fifth (AUDIO: My Dinner with Andrew) Commander Maxil in his sixth, (TV: Arc of Infinity, The Twin Dilemma) Edward Marlow in his eighth, (AUDIO: Other Lives) and Lobus Caecilius (TV: The Fires of Pompeii, The Girl Who Died) and John Frobisher in his twelfth. (TV: Children of Earth)

Duplicates
Sometimes exact doubles of individuals were created for the purposes of espionage or infiltration. The Daleks often employed such techniques, for example with the creation of a a robot double of the First Doctor, (TV: The Chase) and their use of duplicates including Stien, (TV: Resurrection of the Daleks)

Other groups also created robot or android doubles, such as the Kraals, who replicated the Fourth Doctor, Sarah Jane Smith, Sergeant Benton, and Harry Sullivan, (TV: The Android Invasion) the Tarans who crowned Prince Reynart's robot double king in his place, (TV: The Androids of Tara) and Sharaz Jek, who created android doubles of Major Salateen, the Doctor and Peri. (TV: The Caves of Androzani)

A particular type of double was known as an Auton, the plastic agents of the Nestene Consciousness. Among their number include a duplicate of General Scobie, (TV: Spearhead from Space) a duplicate of Mickey Smith, (TV: Rose) and a duplicate of Rory Williams. (TV: The Pandorica Opens/The Big Bang)

In addition, Bill Filer was duplicated by Axos, (TV: The Claws of Axos) Drake created a duplicate of K9, (TV: Jaws of Orthrus) and the Flesh was used to create "Gangers" of both the Eleventh Doctor and Amy Pond, among other characters, (TV: The Rebel Flesh/The Almost People and A Good Man Goes to War) Jason created Dr. Who with the likeness of the Seventh Doctor. (PROSE: Conundrum, Head Games)

A final method of creating duplicates was cloning. A clone of the Sixth Doctor was created by the Forge, (AUDIO: Project: Lazarus) and Martha Jones was cloned by the Sontarans. (TV: The Sontaran Stratagem)

Shapeshifters
Shapeshifting beings often adopted the appearances of other individuals for both malicious and benign reasons. The shapeshifting Zygons often used their shapeshifting abilities to allow them to infiltrate societies they planned to invade or exploit, such as the occasion when the impersonated several people including Harry Sullivan. (TV: Terror of the Zygons) The impersonation of Petronella Osgood began this way also, but the two Osgoods grew close after a deal was brokered between UNIT and the Zygons and the Zygon Osgood's permanently adopted Osgood's appearance. (TV: The Day of the Doctor, The Zygon Invasion, The Zygon Inversion)

Having lost any form of facial identity in the catalysm back in their home system, the Chameleons developed technology which allowed them to adopt the appearance of several people on Earth including Polly Wright and Jamie McCrimmon. While they were using this ability to infiltrate human society and steal further identities, their goal was to permanently adopt these faces to replace their own lost ones. (TV:The Faceless Ones)

The Justice Department Vehicle known as the Teselecta took the form of Grigori Rasputin with green skin, a caretaker, Erich Zimmerman, a Nazi soldier (both with and without a motorbike), Amy Pond, River Song, (TV: Let's Kill Hitler) and the Eleventh Doctor, (TV: The Wedding of River Song)

The Time Lady Romana II chose to take on the appearance of Astra of Atrios when she regenerated. (TV: The Armageddon Factor, Destiny of the Daleks) Omega once used the Fifth Doctor's biodata to take on his form. (TV: Arc of Infinity)

Other shapeshifters include Meglos who took the Fourth Doctor's form, (TV: Meglos) Kamelion, who took on the form of King John of England and, momentarily, the Fifth Doctor,  and Tegan Jovanka, (TV: The King's Demons) and a Kymbra Chimera, which took on the form of the Sixth Doctor and Peri Brown while in the Doctor's TARDIS, (COMIC: Changes)

Other
The Third Doctor travelled to a parallel universe and encountered other versions of Alistair Gordon Lethbridge-Stewart, Liz Shaw, and John Benton. (TV: Inferno) The Tenth Doctor travelled to a parallel universe and encountered other versions of Mickey Smith, Jackie Tyler, Pete Tyler, and the Cybermen. (TV: Rise of the Cybermen) Zagreus and the Eighth Doctor were identical. (AUDIO: Neverland, Zagreus) Townsend, Tepesh, and Winky were projections of the Seventh, Sixth and Fifth Doctors. (AUDIO: Zagreus) The Tenth Doctor transferred his regeneration energy to his hand, and when Donna Noble touched it, she created the Meta-Crisis Doctor. (TV: Journey's End)