Friedrich Nietzsche

Friedrich Nietzsche (AUDIO: Too Many Masters) was a philosopher. He dealt in morality, (AUDIO: The Spectre of Lanyon Moor) and one of his concepts involved a metaphorical abyss, that stared back at you. (PROSE: Uranus)

Nietzsche once declared that "God is dead". When an Ogron uttered these same words after killed their Crab God, Missy sarcastically called them Friedrich Nietzsche. (AUDIO: Too Many Masters)

Evelyn Smythe thought that Aleister Crowley was, at the very best, a cut-price Nietzsche. (AUDIO: The Spectre of Lanyon Moor)

Prentis Duke hated the grey void of hyperspace, as if you looked too hard into it, "it became Nietzche's abyss, grinning back at you." (PROSE: Uranus)

The Seventh Doctor noted that Nietzsche said not to gaze into the void, or something similar, and also said interesting things about fighting monsters; the Doctor found the rest of what Nietzsche said regrettable. (PROSE: Timewyrm: Revelation)

Behind the scenes
In The Dying Days, the Eighth Doctor paraphrases Nietszche's Beyond Good and Evil:
 * "I've gazed into the abyss already, Xznaal, and the abyss gazed into me. It fled from what it saw. Monsters who fight with me should take care." -Eighth Doctor

This is, of course, an inversion of the original quote:
 * "He who fights with monsters should look to it that he himself does not become a monster. And if you gaze long into an abyss, the abyss also gazes into you." -Friedrich Nietzsche

In reality, the infamous quote "God is dead. God remains dead. And we have killed him.", was spoken not by Nietzsche himself, but by a character in one of his books, The Gay Science, in the section The Madman.