Cancer was a class of diseases among humans and other species. It was characterised by uncontrolled division of cells and the ability of these cells to invade other tissues. This unregulated growth was caused by damage to DNA, resulting in mutations to genes that controlled cell division. If untreated, cancers could kill its host.
Cancer cells were even sometimes considered to be immortal. As a result, there was a rumour spreading during Miracle Day that, since everything mortal became immortal, cancer cells became mortal, which Allen Shapiro took as a good enough excuse to start smoking again. (TV: End of the Road)
The First Doctor met the elderly Christian leader Hebron, who was dying from cancer. This revelation humbled him, since until then he had been immersed in self-pity over the loss of the TARDIS and separation from his companions. (PROSE: Byzantium!)
In 1976, Carolyn McConnell had dreams of finding a cure for cancer when she started out as a pre-med student in San Francisco. Some of her passion was diverted to an interest in vampires after the Eighth Doctor and Sam Jones rescued her from one of them. (PROSE: Vampire Science)
In 2011, during the Miracle Day phenomenon, the switch from mortal to immortal had rendered cancer cells mortal, allowing people to smoke freely, although the government kept this information quiet. (TV: End of the Road, WC: Web of Lies)
In the early 21st century, cancer was more common due to high pollution levels. Maria Chavez died from cancer brought on by years of exposure to toxic cleaning fluids. Stephanie had lung transplant surgery done to treat her lung cancer. (PROSE: Cat's Cradle: Warhead)
When Ace was attending the Time Lord Academy on Gallifrey, she discovered that her mother Audrey Dudman had died of cancer. She was warned by her tutor not to try to go back in time and prevent that from happening. (AUDIO: The Lights of Skaro)