Yes, we're pretty sure:
The Doctor's causes of regeneration:
1st: Was apparently growing weak from old age. He collapsed from exhaustion while battling the Cybermen on Mondas.
First Appearance: An Unearthly Child
Regenerated: The Tenth Planet
2nd: The Time Lords punished the Doctor for breaking their laws of non-interference by forcing him to regenerate into his next incarnation.
First Appearance: The Tenth Planet
Regenerated: The War Games/The Night Walkers
3rd: "Died" from the effects of extreme radiation poisoning caused by the Great One's web of Metebelis crystals. Fellow Time Lord, K'anpo Rimpoche saved the Doctor's life by kick starting the regeneration process, which caused him to change into his 4th incarnation.
First Appearance: Spearhead from Space
Regenerated: Planet of the Spiders
4th: The Master indirectly caused the Doctor to fall from the top of the Pharos Project tower, causing him fatal damage. As he lay injured and dying, the Watcher (a being thought to represent something between the Doctor's 4th and 5th incarnations) merged with the Doctor and saved his life by transforming him into his next incarnation.
First Appearance: Robot
5th: After dropping the contents of the antidote for the pathogen, Spectrox Toxaemia, the Doctor saved Peri Brown by giving her the last vial. He then succumbed to the effects of the disease and regenerated.
First Appearance: Logopolis
Regenerated: The Caves of Androzani
First Appearance: The Caves of Androzani
Regenerated: Time and the Rani
7th: Somehow regenerated in a San Francisco hospital's morgue hours after surgeon Grace Holloway, accidentally killed him with anaesthetic and a probe while trying to fix his "heart problem".
First Appearance: Time and the Rani
Regenerated: Doctor Who (1996)
8th: Was killed when the spaceship he was on crashed landed on the Gallifreyan colonial planet called Karn. He was brought back from the brink of death by the Sisterhood of Karn, and regenerated into the War Doctor by drinking a specialised Elixir of Life, so he could fight in the Last Great Time War.
First Appearance: Doctor Who (1996)
Regenerated: The Night of the Doctor
Warrior: After centuries of fighting in the Time War and time locking Gallifrey along with his twelve other incarnations, the War Doctor regenerated after apparently "wearing a bit thin".
First Appearance: The Name of the Doctor
Regenerated: The Day of the Doctor
9th: Absorbed the energy of the Time Vortex from Rose in order to save her life. This caused rapid cellular decay, and he regenerated shortly after in order to save his own life.
First Appearance: Rose
Regenerated: The Parting of the Ways
10th (11th regeneration): Regenerated and healed his body after nearly dying from being grazed by a Dalek's laser beam. Avoided the change into what would have potentially been his 12th incarnation in the nick of time, by directing the transformative energy of the process into his spare hand.
10th (12th regeneration): The Doctor locked himself in a radiation booth and absorbed an amount of rads that would've instantly killed an ordinary man. Held back the process in order to bid a final farewell to his former companions. He eventually regenerated (which destroyed the TARDIS console room) into his 13th incarnation.
First Appearance: The Parting of the Ways
Regenerated: The Stolen Earth/Journey's End, and The End of Time: Part 2
11th: After a near millennia of protecting the people of Trenzalore from many of his old enemies, the Doctor was given a second regeneration cycle by the Time Lords, just as he gave up his life. He used the energy to utterly destroy the Daleks and their entire fleet before returning to the TARDIS in the form of a young man. With the process in its final phase, the Doctor accepted he was always going to be the same person deep down, no matter how many times he changed. He then became a new man a thirteenth time (but regenerated a 13th time), becoming the 12th Doctor.
First Appearance: The End of Time: Part 2
Regenerated: The Time of the Doctor