Conspiracy

A conspiracy was a type of plot, (TV: The Two Doctors) often political in nature, (TV: The Curse of Peladon, Frontier in Space, etc.) made in secret between multiple individuals known as conspirators. (TV: The Twin Dilemma etc.) Conspiracies were often related to treason, sabotage, and terrorism. (TV: The Mutants etc.)
In Ancient Rome, the Doctor appeared to sense some sort of conspiracy, but could not identify it until Vicki causally let slip that she had been involved in a plot with Maximus, Tavius, and Locusta to poison Nero. The latter two of these were pretending to work for Nero while plotting against him. Nobody else outside of this group was supposed to know of these plans, officially, and Vicki seemed to panic one she realised what she’d done. Despite agreeing with the plotters on Nero’s evil, the Doctor was forced to scupper their plans and save Nero’s life in order to preserve the space-time continuum, since Nero’s death could not be rewritten. Nero tricked a slave into drinking the wine to see if the Doctor was telling the truth, and received confirmation when the slaves, choking, collapsed down dead. Unaware of these motivations, the other plotters believed the Doctor to be a friend of Nero following this incident, and deemed Vicki untrustworthy for telling him. (TV: "Conspiracy")
The Sixth Doctor noted that he frequently fought "power-mad" conspirators, though also that they were not as corrupt as the Time Lords. (TV: The Ultimate Foe)
It was something on which the Thirteenth Doctor's view alternated. Though she initially claimed to "love a conspiracy", (TV: Arachnids in the UK) she later said that she did not like conspiracies. She went on to say that the problem with conspiracies was that there was so much to think about. (TV: Kerblam!)
Nazi leader Adolf Hitler responded in his suicide note to allegations of starting World War II by claiming have been provoked into it by a Jewish conspiracy. (PROSE: The Shadow in the Glass) However, the defence did not appear to be taken seriously, and most accounts placed the blame for the war squarely at his feet (TV: Silver Nemeis, Let's Kill Hitler, PROSE: Timewyrm: Exodus, The Spear of Destiny)
Belief in a conspiracy, whether a real or imagined one, was known as a "conspiracy theory". Many of these were published on the internet, inspiring Donna Noble to investigate Adipose Industries, (TV: Partners in Crime) and Clive Finch to keep records on the Doctor, specifically on his ninth incarnation, (TV: Rose) although one account claimed that Clive had photographs of other incarnations, primarily of an incarnation with a scarf. (PROSE; Rose) rewboss, one of the readers of Clive's website, wasn't sure if Clive was a conspiracy theorist and didn't believe that the Doctor was part of a conpsiracy. (PROSE: Have You Seen This Man?) When the site was taken over by a new webmaster after Clive's death, he wrote about the growing conspiracy about the willingness of people to forget the Dummy Massacre, which he speculated was in part due to the uncomfortable truth, the fear even, of something that was being actively hidden from the World Media. (PROSE: The Doctor Was Involved in the Dummy Massacre)
On the Who is Doctor Who? website in early 2006, the webmaster believed there was a government conspiracy growing, as MP Joseph Green had recently had an unexplained weight gain. He also questioned if the government was truly composed of fat cats, feeling that it was time for a change. (PROSE: Rose sighting confirmed)
In 2540, the Daleks conspired with to provoke a war between the space empires of Earth and Draconia, (TV: Frontier in Space) in a strategy named Operation Divide and Conquer. (AUDIO: The Dalek Conquests) The exposure of the conspiracy led to the outbreak of the Second Dalek War. (PROSE: Love and War, Deceit)