Brain

A brain was the central area for thought in most sentient biological entities. All animals had brains of some sort. (TV: Invasion of the Dinosaurs) It was a biological system made from brain cells, which came together to form the mind, a seat for consciousness, complete with memories and intention. (AUDIO: The Vengeance of Morbius)

The Fourth Doctor claimed that a machine as efficient as the human brain would have to be bigger than London and powered by the entire European grid. A Time Lord's brain was even more complex. (TV: The Invisible Enemy)

The Ood had two brains. One was carried in their hands. There was also a giant brain on the Ood Sphere which formed their collective consciousness. (TV: Planet of the Ood)

K9 Mark 2 told Starkey that the second planet in the Montoon system had an "ocean of brains". (TV: Curse of Anubis)

The Morpho were a race of disembodied brains, (TV: "The Velvet Web") as were the Masters of Dorada, (PROSE: The Dream Masters) and the Shoal of the Winter Harmony. (TV: The Return of Doctor Mysterio)

The Mechanistrians were Korads who had their brains placed in machines. (PROSE: Peril in Mechanistria)

Manipulation
Richard Harries experimented with brainwaves. He had sibling rats transfer knowledge through the waves and complete tasks the other had learnt. (PROSE: The Banquo Legacy)

The Fifth Doctor created an anti-dreaming device that stopped the brainwaves associated with dreaming. (TV: Snakedance)

While most brains were natural, once constructed a giant brain to absorb the mental energies of various individuals and compute the equations for a Time Manipulator. (TV: Time and the Rani)

Illness
Miranda Cleaves had a blood clot in her brain, as did her Ganger. Cleaves was cured by a poultice the Eleventh Doctor gave her. (TV: The Almost People)

Dorothy McShane had her brain function checked when she underwent a full medical examination to be a passenger on the Virgil. (PROSE: At Childhood's End)

Transplantation
In certain circumstances, the brain could be transplanted out of the biological entity into another vessel. This was done with Morbius' brain after his body was destroyed. Morbius' ally, Mehendri Solon, had to find a head large enough to fit the brain and only found the right match when he met the Fourth Doctor. (TV: The Brain of Morbius) On Thoros Beta, the surgeon Crozier accomplished significant results in this field, with the brain of the Mentor Kiv. (TV: Mindwarp) On Pete's World, the Cybermen there were created by having the brain transplanted from the human form into the cybernetic suit. (TV: Rise of the Cybermen) The War Chief, his own body being badly deformed, desired to transplant his brain into the Seventh Doctor's body and vice versa. (PROSE: Timewyrm: Exodus)

Lady Cassandra O'Brien.Δ17 was able to survive the destruction of the sheet of skin which formed her "body" because her brain was undamaged, allowing her to constitute a new skin body with another skin sheet from her old human body — this one taken from her backside. Her brain meat expired after she used a psychograft to transfer her consciousness inside the body of Rose Tyler. (TV: The End of the World, New Earth)

swapped Rupert's brain for the brain of a Bandril, and used Rupert to organise his media interests. (PROSE: A letter from the Master)

Other uses
The Clockwork Repair Droids of the 51st century spaceship SS Madame de Pompadour thought they could use the brain of their ship's namesake, Madame de Pompadour herself, to help repair their ship; to this end they opened up time windows back to 18th century France to stalk Madame de Pompadour. (TV: The Girl in the Fireplace)

Mordrega needed to consume human brains to survive. (AUDIO: The Ghosts of Gralstead)

Brain size
The Judoon had rather small brains; a Judoon brain was able to fit in a box that could easily be held in a humanoid palm. (WC: Prequel (A Good Man Goes to War))

According to Tegan Jovanka, most dinosaurs had brains "the size of a pea". (TV: Earthshock)

Power
The Great Power increased the power of Dalek brains, but it killed them shortly afterwards. (PROSE: Doctor Who and the Daleks)

The Doctor's brain
Cybus-type Cybermen of the Cyber Legions determined that the Eleventh Doctor's brain was not compatible for cyber-conversion; as such, they intended to discard it whilst suggesting that other body parts could be of use. (TV: Closing Time) The Doctor claimed to have twenty-seven brains when chatting with Clara, although it was a lie. (TV: The Bells of Saint John) When the Cyberiad attempted to assimilate the Doctor, he managed to retain enough free will to keep just under half of his brain under his control, the Cyber-Planner calling itself Mr Clever controlling an equal amount of the brain. Using a hand pulse, the Doctor managed to purge the Cyber-Planner from his brain. (TV: Nightmare in Silver)