Hypnosis

Hypnosis or mind control was the ability to place others into a state in which they would obey the commands of the hypnotist or believe what the hypnotist told them. Some forms of hypnosis were stronger than others. Memory erasure or alteration also could be accomplished hypnotically.

The Doctor and hypnosis
The Doctor occasionally practised hypnosis.

To break the mind control by the artificial intelligence WOTAN, the First Doctor used it on his companion Dodo Chaplet, leaving her asleep 48 hours long and forgetful of the accident. (TV: The War Machines)

He sometimes did this through eye-fixation. On Necros, the Sixth Doctor tried to perform this form of hypnosis on a mutated victim of Davros' experiments. It failed and he was forced to fight the creature off. (TV: Revelation of the Daleks)

The Third Doctor proved to be able to break a state of hypnosis caused by others: on Jo Grant manipulated by the Master, through a verbal technique (TV: Terror of the Autons) or on the scientists kidnapped by the Sontaran Linx, with the help of an intermittent light. (TV: The Time Warrior)

On other occasions, the Doctor seemed to possess the Master's skill of just talking someone into a state of sleep.

The Fourth Doctor hypnotised Sarah-Jane Smith in order to reduce her oxygen requirements inside a decompression chamber (TV: Terror of the Zygons) or recover information about the entity that had possessed her through a Kastrian ring (TV: The Hand of Fear) simply by laying his hands on her temples.

On Pluto, he once hypnotised one of the Company's guards in this way —and accidentally hypnotised a watching Leela, as well. (TV: The Sun Makers)

On Ribos, instead, the Fourth Doctor used a fob watch to hypnotise a guard of a relic room. (TV: The Ribos Operation)

The Master and hypnosis
As a means to his ends, the Master frequently used hypnosis to have people perform tasks on his behalf. He most commonly did this through suggestion, uttering the phrase "I am the Master and you will obey me". (TV: Terror of the Autons)

While working under the alias of Professor Thascalos at the Newton Institute, the Master hypnotised its director, Charles Percival; he later commented that it had been a long time since he came across a hypnotic subject as good as Percival. (TV: The Time Monster)

The Master failed to hypnotise Jo Grant when she used repeated nursery rhymes to resist. (TV: Frontier in Space)

The Master tried to hypnotise Peri Brown, the Sixth Doctor's companion, using a distracting swinging implement as a focus; it failed, however. (TV: The Mark of the Rani)

He also tried to hypnotise Sabalom Glitz but he failed (TV: Trial of a Time Lord: The Ultimate Foe)

He later hypnotised the Earth on a large scale through use of the Archangel Network, subtly changing people's perception of him. (TV: The Sound of Drums)

On Earth
Passengers of the aeroplane Golf Victor Foxtrot were hypnotised by the Xeraphin after travelling through a time corridor to the Jurassic era. (TV: Time-Flight)

Sarah-Jane Smith was put under a hypnotic trance by Hieronymous. She was told that the Fourth Doctor was an evil sorcerer and that she should kill him with a poisoned needle. The Doctor realised that she was being influenced when she questioned her ability to understand strange languages, which she had never done before. (TV: The Masque of Mandragora)

George Hutchinson was hypnotised by the Malus into helping create conflict in the area. The Malus fed on the psychic energy created through this. (TV: The Awakening)

Magnus Greel granted Li H'sen Chang the power of hypnosis, among others, in return for his services. (TV: The Talons of Weng-Chiang) Professor Brett was hypnotised by WOTAN, his own creation, into aiding the robot's bid to take over Earth. Other factory workers were also hypnotised into producing the War Machines. (TV: The War Machines)

The Weed Creature controlled both Mr. Oak and Mr. Quill through hypnosis. They also received the ability to exhale toxic gas. Both of them were freed by the death of the Weed Creature. (TV: Fury from the Deep)

On Metebelis III and on Earth, the Eight Legs performed hypnosis on a host by attaching themselves to the back. From this position, they could govern the host. (TV: Planet of the Spiders)

Jack Harkness used hypnotic induction to focus Toshiko Sato, Gwen Cooper, Ianto Jones, and Owen Harper on their true memories before using Retcon to rid them of the memory of Adam Smith. (TV: Adam)

The Pied Piper hypnotised several children in order to abduct them, but was foiled by Mr. Smith phoning them all on their mobiles, disrupting the Piper's abilities. (TV: The Day of the Clown)

The Ancient Lights took control of people all over the world through Martin Trueman's invocation of their star signs before Luke Smith stopped them. (TV: Secrets of the Stars)

Miss Myers hypnotised a worker in a nuclear power plant to serve her, and put the rest to sleep. (TV: Sky)

The hologram of Joseph Serf was able to hypnotise people. John Harrison intended for him to use the ability to make everyone buy the SerfBoards. Sarah Jane Smith, likely due to experience, was immune to this hypnosis. (TV: The Man Who Never Was)

On other planets
On Marinus, the Morpho hypnotised the humanoids there into taking them as their rulers. (TV: The Keys of Marinus)

The workers of a gas mining colony were hypnotised by the Macra into gathering them the resources they required. (TV: The Macra Terror)

Alzarian spiders could hypnotise through a venomous bite. One did so to Romana who subsequently aided the Marshmen in their attack on the Alzarian starliner. (TV: Full Circle)

The King Vampire was able to hypnotise the Three Who Rule into a thousand years of service and gave them the power of hypnosis. They used this on Romana, placing her in near-death trance. (TV: State of Decay)

With technology
After the 22nd century Dalek invasion, several humans were fitted with special helmets and dubbed Robomen. They served the Daleks in controlling the population. However, the process was unstable, with a high failure rate: many died on the operating table, and a high percentage of the ones that survived rejected the conversion, going insane as a result and often committing suicide. (TV: The Dalek Invasion of Earth)

The Sontarans made use of hypnosis. Jingo Linx had several humans work for him under hypnotic influence, as did the Sontarans of the Tenth Sontaran Battle Fleet when they controlled ATMOS. The Sontarans also hypnotised UNIT privates Harris and Steve Gray. (TV: The Time Warrior, The Sontaran Stratagem, The Poison Sky)

A Tythonian could use its communicator to hypnotise individuals. Torvin and Edu were hypnotised into returning Erato's communicator to him. (TV: The Creature from the Pit)

The leader of the Sycorax attempted to take humans as slaves using blood control to hypnotise all those with A+ blood. The Sycorax threatened to have them commit suicide if their demands were not met, but the Tenth Doctor pointed out that survival instincts would stop them from doing so. He released them by disabling the control. (TV: The Christmas Invasion)

On Pete's World, Cybus Industries used EarPods to control the population and have them report for Cyber-conversion. (TV: The Age of Steel)

The Berserker pendant allowed its users to control others. (TV: The Mark of the Berserker)