Extermination

Extermination was the goal of the Daleks, who sought to kill all other lifeforms in existence. (TV: Genesis of the Daleks) Though used synonymously with pest control or genocide, (TV: Doomsday, Evolution of the Daleks) the execution of a single lifeform could be referred to as extermination. (TV: The Parting of the Ways) The Daleks' first and foremost instrument of extermination was their personal gunstick located on their weapons platform. Before firing a fatal blast, the Daleks would typically and loudly exclaim "Exterminate!" (TV: Genesis of the Daleks)

Other words used by the Daleks synonymously with extermination were destruction, termination, elimination, obliteration, annihilation, and eradication. (TV: The Chase)

A most prolific subject of the Daleks' hatred was the Time Lord known as the Doctor. As such, most Daleks sought to kill the Doctor on sight. (TV: Remembrance of the Daleks, Dalek, Evolution of the Daleks)

Such was extermination part of the Dalek creed that saying "exterminate" was how the Daleks reloaded their weapons. Phrases that didn't conform to usual Dalek vocabulary, such as "I love you." and "You are different from me." would also be translated into "exterminate" by the casings. (TV: The Witch's Familiar)

Similarily, the Cybermen of Pete's World, whom the Daleks engaged in the Battle of Canary Wharf, (TV: Doomsday) sought to "delete" all those they deemed incompatible for the upgrade to cyber-form. (TV: Rise of the Cybermen/The Age of Steel) Cybermen of N-Space used eradication. (TV: Silver Nemesis)

History
During the closing days of the Thousand Year War on Skaro, the Kaleds made "extermination" of the Thals their battle cry. (TV: Genesis of the Daleks) The Kaleds had been indoctrinated with these ideas from a young age as part of the war effort. (PROSE: Doctor Who and the Genesis of the Daleks)

Davros used "exterminate" as an instruction to attack while he was developing the Daleks. The Daleks adopted the word as their own war cry, (TV: Genesis of the Daleks) though it became less common with succeeding generations between the end of the neutronic war and the rise of the Dalek Empire, when life on Skaro was scarce. In this stage of Dalek history, the First Doctor noted that, while the Daleks did not utter "extermination" too often, the term "trip[ped] so easily off the Dalek tongue". (AUDIO: Return to Skaro)

The Daleks exterminated insects known as zomites, which they regarded as pests. (COMIC: The Daleks Destroy the Zomites)

If a Dalek attempted to exterminate Davros, its self-destruct mechanism would be triggered. (PROSE: Father of the Daleks)

Romana II said "exterminate" when she tasered a Dalek to death on an alternative Gallifrey. (AUDIO: Extermination)

Eve, a survivor of the Last Great Time War, recalled that so many of her people were "exterminated" when her home planet was attacked during the conflict between the Daleks and the Time Lords. (TV: Sarah Jane's Alien Files episode 2, The Mad Woman in the Attic)

The "Metaltron", a survivor of the Time War, was responsible for exterminating two hundred humans at GeoComTex in 2012. The Ninth Doctor, before attempting to kill the lone Dalek, ironically announced "exterminate". (TV: Dalek)

During the 21st century Dalek invasion, the gunstick of one Dalek successfully inflicted a mortal wound against the Tenth Doctor, who was forced to regenerate, but used his severed hand to keep himself from changing form. (TV: The Stolen Earth/Journey's End)

Following total event collapse, a Stone Dalek succeeded in landing a hit on the Eleventh Doctor. However, due to the Dalek's weakened state, the Doctor survived. (TV: The Big Bang)

After the Twelfth Doctor had stolen Davros' chair, Dalek control attempted to exterminate him but he survived thanks to the chair's force field. (TV: The Witch's Familiar)

When a Dalek Executioner destroyed the belongings of his exes that he had saved, Nick thanked the Dalek for what he called "therapy". Asked to explain, Nick answered "ex... terminated", to which the Dalek promptly shot him without saying the word. (TV: Eve of the Daleks)

Other references
On Lakertya, Beyus warned Melanie Bush against antagonising the First Rani, claiming that she had only to press a button for every Lakertyan to be exterminated. Mel quipped that she herself could nominate a few candidates for extermination. (TV: Time and the Rani)

Behind the scenes

 * Archive audio of Nicholas Briggs exclaiming "Exterminate!", originally recorded for The Parting of the Ways, is used to represent the Daleks in The Lego Batman Movie.