According to the Second Doctor, touch was one of the five senses of human beings. (TV: The Evil of the Daleks)
The Tenth Doctor observed that, as Kaled mutants were sealed inside their casings, the Daleks could not touch. (TV: Doomsday) However, this was not strictly true; as Daleks could open their casings, enabling the mutants within to make physical contact. (TV: Daleks in Manhattan)
During the Last Great Time War, the Daleks evolved so that they could use the background radiation of time travellers as a power supply. Out of sympathy, Rose Tyler placed her hand on the battered casing of the "Metaltron", which resulted in the Dalek being revitalised. However, this also infused it with Rose's human DNA, which led the Dalek to self-destruct. While Rose sustained only a minor burn to her hand, another person was burst into flames when they touched the Dalek earlier. (TV: Dalek)
Similarily, the Genesis Ark, a Time Lord prison ship, could only be opened by the handprint of a time traveller. As the Cult of Skaro were aware, they attempted to threaten Rose into making contact with it. Ultimately, however, the Ark was touched by Mickey Smith, who inadvertently fell against it during an attack on the Daleks. (TV: Doomsday)
Victims of the Empty Child plague transmitted their affliction with a touch. (TV: The Empty Child) Similarily, the new humans created by the Sisters of Plenitude transmitted all the diseases they carried with a touch, proving fatal for those they came into contact with. (TV: New Earth)
The Abzorbaloff absorbed his victims by touching them. While disguised as "Victor Kennedy", he warned people against touching him, claiming to suffer from eczema. Whilst in the process of being absorbed, Ursula warned Elton Pope not to touch her. (TV: Love & Monsters)
Mother Doomfinger of the Carrionites demonstrated the ability to kill with a "touch of the heart", placing her finger on the chests of her victims. (TV: The Shakespeare Code)