Dalek Caan was one of the four Daleks of the Cult of Skaro. Like the other members, he thought like the Daleks' enemies in order to find new ways of defeating them. He had a mind of his own and could imagine and think for himself.
Battle of Canary Wharf
Dalek Caan was one of the three Standard Daleks who were created to follow the Cult's leader: the supreme Dalek Sec. During the Last Great Time War between the Daleks and the Time Lords, the Cult took the Genesis Ark and fled the war into the Void, resurfacing later in London in 2007.
Arriving in 2007, Caan, Jast, and Sec scanned the brain waves of Dr. Singh and discovered another species had invaded Earth. Upon discovering it was Cybermen, the Cyber-Leader declared war while the Cult claimed it to be pest control. Caan took part in the Battle of Canary Wharf while the Genesis Ark (accidentally activated by Mickey) released millions of Daleks onto Earth. Because they had been through the void, they were covered in void stuff. The Doctor was able to open the rift the Cybermen had come through and reverse it, sucking in all beings covered in void stuff. As the Daleks were sucked into the Void, Dalek Caan and the rest of the Cult activated an emergency temporal shift and escaped. (DW: Army of Ghosts/Doomsday)
The Final Experiment
The Cult ended up in New York City in 1930 and recruited Mr. Diagoras, the head of construction for the Empire State Building. He kidnapped people for their research and for what they called the "Final Experiment". During their time in 1930, Dalek Caan served at the Cult's connection to Diagoras. Eventually, Caan took Diagoras to see their leader Sec who merged with Diagoras in his casing to become the first Human-Dalek. (DW: Daleks in Manhattan)
After Sec became a Dalek-Human, he showed feelings that their creator, Davros, was wrong about removing emotions and that the deaths at Hooverville were wrong. Caan and the other members felt that the plan Sec had for the new Daleks was unacceptable; it would change everything that makes a Dalek a Dalek and the Daleks would no longer be supreme. Feeling Sec was no longer a Dalek, Caan led a mutiny with Dalek Jast and Dalek Thay to imprison Sec, having poured a different gene solution into the Dalek-Humans than Sec had wanted, making the new bodies 100 percent Dalek.
Dalek Caan made himself Controller and became connected with the Dalek-Human army. When Thay and Jast ordered the new Daleks to destroy the Doctor, they questioned orders and the Doctor explained that he got in the way of the gamma strike which brought them to life, his DNA becoming mixed with theirs, giving them a little freedom. When a battle broke out between the Daleks and the Dalek-Humans, Jast and Thay were destroyed. Caan saw the new Daleks as failures and killed the entire species.
Caan was the last member of the Cult and, by extension, the only survivor of the entire Dalek race, therefore he was narrowed down to be the entire Dalek species. The Doctor confronted him and offered Caan help and compassion, being that he didn't want to cause a genocide. Caan activated an emergency temporal shift and escaped. (DW: Evolution of the Daleks)
Insanity
I flew into the wild and fire. I danced and died a thousand times.
It is revealed that Dalek Caan teleported to the Time War, despite it being time locked. Once there, he found and saved Davros, something which the Doctor himself had failed to do. After the Daleks moved Earth to the Medusa Cascade, Dalek Caan resided on the Dalek spaceship, giving cryptic information to Davros.
The supreme Dalek on board the spacecraft claimed that Caan was insane, a notion which Davros dismissed, claiming that nothing would be possible without Caan. This shows that Caan had a certain amount of respect from Davros. However, Davros acknowledges that he had become mad due to the strain of time-traveling directly into the Time War, corroborated by Caan's insane laughter and talking in seemingly precognitive riddles in an almost sing-song voice. (DW: The Stolen Earth)