The first appearance of a Dalek on Doctor Who was during the episode “The Daleks/The Mutants/The Dead Planet.” This was the episode right after “An Unearthly Child” and still had William Hartnell as the Doctor. During this episode Barbara gets separated from the rest of the group, and is threatened by the metal arm with a plunger cup.
After this episode the Daleks portray in around 28 more episodes spanning the time between William Hartnell and Peter Capaldi. The ironic evolution of the Dalek in the series is the amount of times that the Doctor believes there are no more Daleks during the reboot. During Christopher Eccleston, the Doctor and Rose discover a Dalek being held by a billionaire, and at the touch of Rose, it comes back to life.
During the episode “Doomsday,” Rose, Mickey, the Doctor and Jackie band together to face the Daleks and Cybermen that have come to invade the Earth. The Daleks were hiding in a sphere located in the basement of Torchwood, while the Cybermen were hiding upstairs in the construction zone. The Daleks needed the touch of the Doctor or one of his companions to open the Genesis Ark that was a prison to thousands of Daleks. The episode ends with the Doctor sending the two species into the void, and loosing Rose to the other dimension.
One of my favorite episodes with the Daleks is the “Victory of the Daleks” when the Doctor is Matt Smith and the companion is Amy. During this episode, it is discovered that Winston Churchill was using a “scientific advance” by a Professor Edwin Bracewell. They were called the “Ironsides” but were quickly recognized by the Doctor as the Daleks. The Doctor tries over and over to get the Daleks to admit that they weren’t invented on Earth and to tell what their purpose was. After the Doctor yells “I am the Doctor and you are the Daleks,” the Daleks on Earth become hostile and begin to act just as they did before. The Doctor follows the Daleks to their ship called the Crucible.
The Daleks needed to open the Progenator, which held pure Dalek DNA, to restore the race. The Progenator needed the Doctor to open it. The Doctor wont open it to keep the race from going, until the Daleks turn on the lights in London just before an air raid, which stops him in his tracks. There are five Daleks that emerge from the Chamber, The Scientist, The Drone, The Strategist, The Eternal, and The Supreme. The Daleks end up getting away as the Doctor goes down to London to save the planet.
The Doctor’s love for the planet may save it over and over again, but it continues to let his biggest enemy get away time and time again.