The Devil

Satan, usually known as the Devil, was, according to Toby Zed, "fury and rage and death". (TV: The Satan Pit) Oswald Danes once joked that, should the Devil walk the Earth, he'd certainly work in PR. (TV: Rendition) According to the Tenth Doctor, "more religions than there are planets in the sky" had devils, also known as beasts, including the Arkiphets, Quoldonity, Christianity, Pash Pash, New Judaism, San Klah and the Church of the Tin Vagabond. Neoclassic Congregational didn't have a devil per se, only "the things that men do", which the Doctor claimed was the "same thing in the end". (TV: The Satan Pit)

Some associated Hell with the Devil. Winston Churchill once mentioned that "If Hitler invaded Hell, I would give a favourable reference to the Devil." (TV: Victory of the Daleks)

Many people were afraid of the Devil. During an invasion of New York City in the 21st century, a Cerebravore used Hector's fear of the Devil against him. Hector believed that the Devil came for him because he knew his sins. (COMIC: Revolutions of Terror)

Origins of the myths
Several beings and groups were a possible source for the idea of Satan.

The Dæmons, a horned race from the planet Dæmos, were believed by the Third Doctor to be the inspiration for Satan based on their experiments on humanity. (TV: The Dæmons) Likewise, the Demoniacs were another species believed to have influenced human society. (PROSE: Mean Streets)

The Greek Immortal Hades, a supposed lord of the underworld, was also known to call himself Satan. (PROSE: Deadly Reunion)

The Fourth Doctor believed that Sutekh had called himself several names, including Satan. (TV: Pyramids of Mars)

The Beast said that he was the origin of, if not the actual Satan, and all similar entities on all worlds. (TV: The Impossible Planet / The Satan Pit) The Tenth Doctor found the Beast, in particular his claim to have existed before the universe, a challenge to his own belief system. (TV: The Satan Pit) He did eventually refer to the Beast as "the devil". (TV: Planet of the Ood)

Mistaken identity
On other occasions, entities were mistaken for Satan accidentally.

When Momus stole Joan of Arc from Earth, she believed it was a trick of the Devil. (PROSE: The Lonely Computer)

In 1140, the Krillitane in Worcester were thought to be the Devil. (PROSE: The Krillitane Storm)

In 1588, the Vituperon posed as the Devil. (AUDIO: The Devil's Armada)

In 1928, when Angelo Colasanto learned of Jack Harkness' immortality, he thought he was the Devil. He was captured and killed repeatedly, though some thought he was a miracle instead of the Devil. (TV: Immortal Sins)

In 1930, a Hooverville resident called a Dalek that appeared above the settlement "a devil in the sky". (TV: Evolution of the Daleks)

When Fitzroy contacted Bryn Williams and tried to make a deal with him in 2009, Bryn assumed it was the Devil. (AUDIO: The Devil and Miss Carew)

In his speech to the Clerics in which he told them that the Eleventh Doctor was a living breathing man, Colonel Manton said that the Doctor was not, among other things, the Devil. (TV: A Good Man Goes to War)