Evil

Evil was the concept or force perceived as being the opposite of what was good, both of them being part of moral duality. However, like good, evil could be perceived differently with conflicting views; as such, the Seventh Doctor claimed evil had no name, (TV: The Curse of Fenric) and the Twelfth Doctor later claimed that "hardly anything [was] evil, but most things [were] hungry." (TV: The Pilot)

In the distant past, the Grey Man's people imposed duality onto the first humanoids to evolve, resulting in them destroying themselves in chemical warfare. The Grey Man later created Cathedral as a metacultural engine that introduced "greyness" and "doubt" into the universe. (PROSE: Falls the Shadow)

At the end of the Thousand Year War, Ronson told the Fourth Doctor that the Scientific Elite believed Davros had changed the nature of their research to something immoral and evil, which later resulted in the creation of the Daleks. (TV: Genesis of the Daleks)

The Time Lords did not believe in nor gave much thought to the concepts of good and evil, although the Doctor had always maintained that evil was a real force. (PROSE: Strange England, AUDIO: The Guardians of Prophecy, COMIC: A Groatsworth of Wit) When he was first put on trial, the Second Doctor used a Thought Channel to justify his interference in the universe by showing the Time Lord tribunal some of the evils he'd fought, including the Quarks, the Robot Yeti, the Ice Warriors, the Cybermen, and the Daleks. (TV: The War Games)

In his travels he met many "embodiments" of evil, including the Black Guardian, (TV: The Armageddon Factor) the Mara, (TV: Snakedance) Malador, (AUDIO: The Guardians of Prophecy), the Beast (TV: The Impossible Planet) and Fenric, whom the Doctor told Ace was one of two forces, only good and evil, that existed before the beginning of all time and space. (TV: The Curse of Fenric) The Ninth Doctor described the Shadeys as "something evil," mentioning to Rose Tyler that "some people don't believe in evil... They say it's all subjective. No absolutes," and as a rebuttal to this, he told Rose to "take a look" at the Shadeys. (COMIC: A Groatsworth of Wit)

The Third Doctor described the Master as "the personification of evil", (TV: The Sea Devils) the Fourth Doctor later calling him the "quintessence of evil," (TV: The Deadly Assassin) while Borusa told the Master that he was "one of the most evil and corrupt beings [that] Time Lord race [had] ever produced." (TV: The Five Doctors) Even when Melanie Bush told him he was "utterly evil," the Master replied "thank you."

In truth, anyone was capable of both good and evil, as the Master pointed out when he revealed to the Sixth Doctor that the Valeyard was a future version of him:

"There is some evil in all of us, Doctor, even you. The Valeyard is an amalgamation of the darker sides of your nature..."

- The Master

While the Doctor often tried to be a force for good, his methods could be seen as evil, causing other races to raise arms in fear against him, (TV: A Good Man Goes to War) with an alliance including several of his enemies imprisoning him in an attempt to prevent the end of the universe. (TV: The Pandorica Opens) Several individuals considered the Doctor's good to be their evil, including Sutekh (TV: Pyramids of Mars) and the Black Guardian. (TV: Mawdryn Undead)

Behind the scenes
The Universal Databank identified six types of evil which the Doctor has fought against. These were as follows:
 * 1) Those motivated by greed — Kal; Aydan, Eyesen and Kala; Forester; Bennett; Sevcheria; El Akir; Johnny Ringo; Grey; Samuel Pike; Theodore Maxtible; Maurice Caven; Dent; Irongron and Bloodaxe; Eckersley; Lupton; Kellman; Federico; Henry Palmerdale; the Usurians; Graff Vynda-K; Xanxia; Vivien Fay; Grendel; Adrasta; Tryst and Dymond; the Gaztaks; Rorvik; Morgus and Stotz; the Chief Officer, the Mentors; Kara; Doland; the Bannermen, Keillor; Peinforte;
 * 2) Misguided fanatics — Tegana; Tlotoxl; Maximilien Robespierre; Eric Klieg and Kaftan; Charles Carrington; Eric Stahlman; Hepesh; George Trenchard; Charles Grover; J. P. Kettlewell and Hilda Winters; Sorenson; Harrison Chase; Hieronymous; Taren Capel; Maximillian Stael; Kassia; George Hutchinson; Timanov; Dastari; Helen A;
 * 3) Those motivated by megalomania and/or a desire for conquest — the Master; the Rani; Borusa; Morbius; Animus; Eldrad; Meglos; Monarch; Mestor; the Borad; Kroagnon; Kane; the Ice Warriors; the Voord; the Drahvins; the Macra; the Dominators; the Krotons; the War Lords; the Nestene; Axos; the Zygons; the Kraals; the Krynoids; the Nucleus; the Movellans; the Nimon; the Terileptils; the Tractators; WOTAN; BOSS; Zaroff; Salamander; Tobias Vaughn; Magnus Greel; Morgaine; the Daleks; the Cybermen; the Sontarans;
 * 4) Those who seemed to be evil incarnate — the Celestial Toymaker; the Great Intelligence; Sutekh; the Mandragora Helix; the Fendahl; the Black Guardian; the Shadow; the King Vampire; the Mara; the Gods of Ragnarok; the Destroyer; Fenric;
 * 5) Those driven to become evil by a cruel twist of fate — Omega; the Wirrn; Xoanon; Scaroth; Mawdryn; Sharaz Jek; the Silurians and Sea Devils;
 * 6) Those motivated by factors beyond human notions of good and evil — the Dæmons; Kronos; the Xeraphin; the Eternals.