A is for... Androids

The words "android" and "robot" are often used interchangeably in Sci-Fi, and Doctor Who is no exception. Both refer to mechanical beings. Androids are often used to describe facsimiles of real humanoid beings, whilst not all robots are shaped like people with arms and legs. The following is a list of androids encountered by the Doctor over the years. Either they have been specifically described as "androids" on screen, or they fit the mechanical copy of a human definition.

Android First Doctor - The Chase (1965).
The Dalek execution squad sent to hunt the Doctor and his companions through Space and Time decided to create a mechanical replica of the Doctor to infiltrate and kill the time-travellers.
It was only when it misidentified Vicki as Susan that the travellers realised which Doctor was the fake one. The Doctor tore out its circuits. In order to fool the Daleks, the Doctor pretended to be the android, but they knew it had already been destroyed.

Kraal Androids - The Android Invasion (1975).
Exact replicas of the inhabitants of the English village of Devesham, where the UK Space Defence Station was based. They were copied from the brain scans of the human astronaut Guy Crayford. As well as the villagers, he had also provided details of the Station personnel - including members of UNIT such as Lt. Harry Sullivan and RSM Benton.
The Kraal plan was to replace the real population with their android copies, and these would be used to spread a virulent plague that would wipe out the human race and so allow for an unchallenged invasion. The Doctor realised something was wrong when he and Sarah saw a UNIT soldier throw himself to his death in the countryside near the village - only to turn up unharmed a short time later.
The Kraals also created copies of the Doctor and Sarah. The Doctor used the Station's transmitter dish to broadcast a signal that deactivated the androids.

Taran Androids - The Androids of Tara (1978).
The planet Tara had suffered a terrible plague that decimated the population. Androids were created to carry out menial work. The ruthless political machinations of the ruling families also led to the creation of replicas. The Crown Prince, Reynart, had one android created of himself. This was intended to deflect assassination attempts. When Reynart was captured by Count Grendel, the Doctor fixed up the android to take his place at the appointed hour and so not miss out on his coronation. Grendel had a copy of the Princess Strella made - to kill Reynart at the ceremony. The Doctor spotted that it was a fake when he heard something short inside it. Strella just happened to look like Romana, and Grendel had another android made of her to lure the Doctor into a lethal trap. It was destroyed by K9.

Movellans - Destiny of the Daleks (1979).
I would class the Movellans as androids rather than robots, as they are all physically unique. Robots would have a more uniform appearance.
The Movellans went to war against the Daleks and both races hit a stalemate. They tried to enlist first Davros, then the Doctor to help break this stalemate, but eventually developed a virus that attacked the Daleks and so gained the upper hand.
Movellans could be easily deactivated by removing a power pack from their belts. They could be reprogrammed to attack each other. They could also be confused by ultrasonic sound.
See also "M is for... Movellans".

Urbankan Androids - Four to Doomsday (1982).
The Urbankans themselves were androids. This is how the Ministers Enlightenment and Persuasion could appear exactly as the drawings Tegan had made to show typical Western Earth fashions.
Monarch's ship contained a number of people who had been taken from Earth during his previous visits - prehistoric Aboriginals, Athenian Greeks, Imperial Chinese and Mayans. These were all android copies of the originals. Many were only basic models, designed to carry out menial tasks, whilst others maintained the personalities of the original person.
To prevent revolt, Monarch had programmed the androids so they could never act in unison - something which the Doctor used against him. After Monarch's death, the androids decided to set off and create a new home on some alien planet.

Terileptil Android - The Visitation (1982).
The Terileptils were lovers of art and beauty, despite being a belligerent, war-like race. Their androids were designed to look ornate and beautiful, as well as being hard-working and walking weapons. They had a powerful laser weapon built into their hands.
Once stranded in 1666 England, the Terileptil escaped convicts disguised their android as Death - the Grim Reaper - to scare the locals away from interfering in their activities. The Terileptil leader sent the android to capture the TARDIS. Nyssa created a device which shook it to pieces.

Cyberman Sentinels - Earthshock (1982).
Quite basic machines, with featureless faces, these androids were programmed to prevent anyone from tampering with the bomb which the Cybermen had planted to destroy a forthcoming conference. Their weapons totally disintegrated their victims. The Doctor knew that if Commander Scott's men were to attack the hatch protecting the bomb then this would cause conflict in their programming. They had to protect the hatch, but equally had to protect themselves in order to carry out their orders.
Concentrated firing destroyed both sentinels.

Kamelion - The King's Demons (1983), Planet of Fire (1984).
Created by a race who had invaded the planet Xeriphas, it had been left behind and was found by the Master. He found that it could take on the appearance of anyone willed upon it by himself. Seeing the opportunities it presented, he first tried to use it to mimic King John in order to sabotage the Magna Carta, and so change world history for his own ends. The Doctor could equally impose his will on Kamelion, and was able to take control. It joined the TARDIS crew for a time, until the Master once more imposed his will upon it. Knowing that it would always be susceptible to malign influence, it asked the Doctor to destroy it, which he did - shooting it with the Master's Tissue Compression Eliminator.
See also "K is for... Kamelion".

Sharaz Jek's Androids - The Caves of Androzani (1984).
Most of Jek's androids were basic, featureless models, which he used to handle the deadly raw Spectrox plants, or to act as his own private army. They were programmed to kill anyone not protected by a special belt plate. They were also programmed only to target human beings - so failed to see the two-hearted Doctor as human when they scanned him in X-Ray vision.
Jek also created some exact replicas of real people. His copy of Lt. Salateen was able to fool General Chellak for many months, after he abducted the real soldier and placed his android copy in his HQ. He also made copies of the Doctor and Peri, which replaced them in front of Chellak's firing squad.

Karfelon Androids - Timelash (1985).
Ornate blue faced androids with sing-song voices, these androids were presumably created by the Borad on the planet Karfel. As well as acting as servants, they could also be used to attack people.

The Kandy Man - The Happiness Patrol (1987).
Created by Gilbert M, the Kandy Man was designed to look like the boiled sweets that he enjoyed making. Quite sadistic, he used these to kill people - the enemies of Helen A, who ruled the Earth colony on Terra Alpha. It was susceptible to heat, and the Doctor was able to stick its feet to the floor with lemonade so that he could make his escape. When Helen A's rule began to crumble, the Kandy Man tried to flee through the sugar tunnels beneath the colony. The Pipe People, original inhabitants of this planet, activated the machinery to flood the pipes with molten sugar - destroying the Kandy Man.
See also "K is for... Kandy Man".

Trin-E and Zu-Zana - Bad Wolf (2005).
Androids which hosted a lethal version of What Not To Wear on the Game Station in the year 200, 100 AD. They were based on the TV show's original presenters in the early 21st Century - Trinny Woodall and Susannah Constantine. Captain Jack Harkness came up against them. After redesigning his wardrobe, they moved onto what they called the "face off" - quite literally in this sense. Jack destroyed them with a compact laser he had somehow hidden about his naked person.

Anne-Droid - Bad Wolf and Parting of the Ways (2005).
Host of the lethal version of The Weakest Link on the Game Station. It was based on that programme's original presenter - Anne Robinson. Losing contestants were vapourised by a beam emitted from the droid's mouth, but the Doctor later discovered that this was actually a form of teleport. People were being sent to the Dalek fleet - to be turned into new Daleks. Captain Jack reprogrammed the Anne-Droid to attack the Daleks when they invaded the Game Station, but it was then exterminated.

Clockwork Droids - The Girl in the Fireplace (2006) and Deep Breath (2014).
Ornately designed clockwork androids designed to carry out maintenance on spaceships from Earth in the 51st Century. When the spaceship SS Madame de Pompadour was wrecked in an ion storm, the droids began to repair it using anything that came to hand. This included parts of the human crew. They worked out that to repair the controlling computer they would need the brain of the real Mme de Pompadour, mistress of King Louis XV of France. They created time windows and were able to visit her at different points in her life, scanning her brain each time. Her brain would be harvested when she reached the same age as the ship. The Doctor cut off the droids from the time windows and they deactivated, no longer able to complete their work.

The Twelfth Doctor and Clara met another batch of clockwork droids in Victorian London - this time from the SS Marie Antoinette. Led by the Half-Face Man, they had been stranded on Earth for thousands of years, and stole genetic material to make themselves into human beings. Much of this came from the patrons of a restaurant they ran, built around their escape pod. Over the centuries they had developed a purpose - to become human so that they might find the Promised Land. The Half-Face Man believed himself to be human. He was almost certainly pushed to his death from the escape pod - being impaled on the top of the tower popularly known as Big Ben, after the Doctor failed to get him to commit suicide.
See also "C is for... Clockwork Droids".

Professor Edwin Bracewell - Victory of the Daleks and The Pandorica Opens (2010).
A brilliant scientist working with Winston Churchill on weapons that would win Britain the Second World War. He claimed that ideas just came to him. His greatest achievement were the Ironsides - mobile war machines - which the Doctor instantly recognised as Daleks.
It transpired that he had not created the Ironsides, but they him. He was an android with full memories of a life lived in Paisley, Scotland. He helped the Doctor and Winston battle the Daleks once the truth was revealed - fitting out a squad of Spitfires that could travel in space to attack the Dalek saucer. However, he had been fitted with a powerful bomb that could destroy the entire planet, and had no way of shutting this down. Amy Pond appealed to what humanity the Daleks had given him to stop the countdown. He fully expected to be destroyed by the Doctor after the Daleks had departed, but he was allowed to go free. Some months later, he was still working alongside the Prime Minister when a strange painting was found in France - a Van Gogh image of an exploding TARDIS.
See also "B is for... Bracewell, Prof".

Shakri Android - The Power of Three (2012).
Android facsimile of a little girl that was placed on Earth to monitor the population's response to the mysterious small black cubes that appeared everywhere one night. She based herself in the hospital where Rory Williams worked, which was also where the Shakri had a portal to their extra-dimensional spacecraft. Patients were abducted from here so that the human anatomy could be studied for weaknesses. The girl acted as a conduit for the signal that activated the cubes after months on Earth.

Tricky Van Baalen - Journey to the Centre of the TARDIS (2013).
Poor Tricky only thinks he is an android - a cruel joke played by his bored siblings on their long space voyages seeking salvage. He had been injured in an accident, losing his memory, and had been given cybernetic implants to save his life. Jealous that he was their father's favourite, his brothers convinced him that he was actually an android. The Doctor forced them to admit the truth.

Invisible Android Assassins - The Witch's Familiar (2015).
Invisible androids which assassinate. Not a lot more you can say about these - except that they feature in a story told to Clara by Missy, and she isn't sure which Doctor it was who encountered them. The story may be entirely apocryphal, so they might not even exist at all - simply made up by the Master to illustrate a point.