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A hug was a social expression which generally involved one or more individuals fully embracing others.

The Ninth Doctor once voiced an affection for hugs, claiming he would hug anybody, (TV: The Long Game) and gave them out to comfort others, (TV: Father's Day) or when in moments of joy. (TV: The Doctor Dances, Boom Town, Bad Wolf)

Mickey Smith shared a hug with Rose Tyler when he reunited with her in Cardiff. Observing them, Captain Jack Harkness asked the Doctor why he did not give him hugs, to which the Doctor told him to buy him a drink first. (TV: Boom Town) Aboard the Game Station, the Doctor shared a hug with Captain Jack upon learning from him that Rose had not been disintegrated but transmated. (TV: Bad Wolf)

Rose hugged the Doctor after he rescued her from the Daleks and offered one to Captain Jack when he requested a hug; though he claimed that he was asking the Doctor, Jack nevertheless hugged Rose. Later, after the Doctor sent Rose back home for her protection, Rose tearfully hugged Mickey Smith. (TV: The Parting of the Ways)

Following their confrontation with the Beast, Rose hugged the Tenth Doctor in The TARDIS. (TV: The Satan Pit)

The Tenth Doctor and Donna Noble shared a hug after reuniting in Adipose Industries. Later, by the TARDIS, Donna and the Doctor almost hugged again before Donna remembered to return her mother's car keys. (TV: Partners in Crime)

Rose hugged the Doctor after he regenerated but kept the same face, with Donna offering one to Captain Jack.

You can hug me, if you want. No, really. You can hug me.Donna Noble. [Journey's End (TV story) [src]]

Jack hugged Mickey when they reunited aboard the Crucible before Mickey decided that that was "enough hugging". After the TARDIS towed the Earth out of the Medusa Cascade, Jack hugged Sarah Jane Smith only to be pulled aside by Donna who hugged him herself. Back on Earth, Sarah Jane gave the Doctor a hug as she said goodbye to him. (TV: Journey's End)

Whilst aboard Demons Run, Rory Williams granted the Eleventh Doctor permission to hug Amy Pond before deciding it was "enough hugging". (TV: A Good Man Goes to War)

In River Song's World, Amy hugged the Doctor after reuniting with him, having missed him. Amy later shared a hug with River Song after learning from her that the Doctor had survived his supposed death at Lake Silencio. (TV: The Wedding of River Song)

The Eleventh Doctor hugged Clara Oswald when he rescued her from his time stream. (TV: The Name of the Doctor)

The Thirteenth Doctor also displayed a fondness for hugs. She immediately hugged Yaz's mother, Najia Khan, upon meeting her. (TV: Arachnids in the UK)

The Twelfth Doctor decides hugging isn't for him. (TV: Deep Breath)

In contrast, the Twelfth Doctor held a strong distaste for hugs as they made him feel uncomfortable, (TV: Deep Breath) protesting to Clara Oswald when she attempted so that he was "against the hugging." (TV: Listen) This incarnation of the Doctor would, however, voice that hugs were a good way to smell someone's hair as he hugged Clara to comfort her after she was almost shot. (PROSE: The Blood Cell) The Doctor explained to Clara his belief to "never trust a hug", claiming it was "just a way to hide your face." (TV: Death in Heaven)

Hiding the loss of Danny Pink, Clara concurred as she hugged the Doctor before parting ways. (TV: Death in Heaven) After reuniting, the Doctor began to accept Clara's attempts to hug him over time, (TV: Last Christmas, The Woman Who Lived, Face the Raven) and even started hugging her on the odd occasion. (TV: The Magician's Apprentice, The Girl Who Died) By the time he reunited with Maxwell Edison, the Doctor had accepted being a hugger and gave a loving hug to Max. (COMIC: The Stockbridge Showdown)

The Twelfth Doctor, Bill Potts and Nardole shared a group hug, which Nardole called a cuddle, when he joined in on Bill's hug with the Doctor, when she discovered she was still alive. When Bill earlier hugged the Doctor, on finding out he was blind, he urged her not to "get all gooey on me", as he claimed it was a temporary condition. (TV: Oxygen) Before his regeneration, the Doctor shared another cuddle with Bill and Nardole's glass avatars. (TV: Twice Upon a Time)

When Missy opted to "stand with the Doctor", she tricked her predecessor into hugging her, discreetly stabbing him in the back so he would be forced to regenerate into her. (TV: The Doctor Falls)

In the Starless world, Rory Williams said goodbye to Lancelot via a hug. (AUDIO: The Last King of Camelot)

Jack Harkness gave Graham O'Brien a hug whilst mistakenly believing him to be the Doctor. (TV: Fugitive of the Judoon)