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)
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)
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, the Rani 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)
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. His 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 Kiev. (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 Ood had two brains. One was carried in their hands. There was also a giant brain on the Ood Sphere. (TV: Planet of the Ood)
The Morpho were a race of disembodied brains. (TV: "The Velvet Web") The Masters of Dorada were a race of disembodied brains. (PROSE: The Dream Masters)
K9 Mark 2 told Starkey that the second planet in the Montoon system had an "ocean of brains". (TV: Curse of Anubis)
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. (TV: The End of the World, New Earth)
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)
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))
The Mechanistrians were Korads who had their brains placed in machines. (PROSE: Peril in Mechanistria)
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)
The Great Power increased the power of Dalek brains, but it killed them shortly afterwards. (PROSE: Doctor Who and the Daleks)
The Shoal of the Winter Harmony resembled disembodied brains in their natural form. (TV: The Return of Doctor Mysterio)