J K Rowling is pretty active on Twitter, and often enough releases new canon information there.
However, the vast majority of her tweets are completely unrelated to Harry Potter.
While not necessary, compiling an extensive list yourself is also good :-)
This list should be complete as of December 2016, though it is very possible that some tweets were missed.
This list was started by @Alexwchan using some Python scripts that used the Twitter API to get a complete list of JK Rowling’s tweets. Those scripts, in a very rough form, are on GitHub. This answer is now a community wiki. People should feel free to update it.
In order to properly fit everything with links, this has been divided into two separate answers. This one will only focus on the tweets which aren't related to the Fantastic Beasts film.
Per Accio Quote rules, only information in quotation marks is from JKR herself – everything else is my paraphrasing. Links throughout.
A complete copy of the original text of all of the tweets has been compiled elsewhere (1, 2, 3, 4, 5).
Although he was gay, Dumbledore didn’t experience homophobia in the magical world. “The wizards don't give a damn – it's all about the magic for them.”. Hogwarts was a safe space for LGBT students. Likewise, race wasn't an issue either.
Anthony Goldstein (a Ravenclaw student in Harry’s year) was Jewish. He wasn’t the first or only Jewish student in the school, but he got special mention because he was one of the original forty students. His name comes from one of Rowling's friends.
On the topic of religion, the only religion she didn’t imagine at Hogwarts was Wiccan. (Because it's "a different concept of magic".
Fluffy was “repatriated to Greece” by Dumbledore.
Ron's Patronus is a Jack Russell.
Moaning Myrtle's full name is Myrtle Elizabeth Warren. The name was chosen to match the time period and has nothing to do with the US Senator of the same name.
Of the two Weasley twins, Fred was born first.
Regarding Lupins death: "Arthur lived, so Lupin had to die. I'm sorry. I didn't enjoy doing it. The only time my editor ever saw me cry was over the fate of Teddy."
Harry intentionally didn’t name a child ‘Remus’, so that Teddy could use the name for his own son. Harry only "chose to perpetuate the names of the two who had nobody in their families to do so." He didn't name his kid elvendork becuase Rowling wanted to save the name for herself in case she had a fourth child.
Madam Pince comes from a childhood fear of scary librarians. (I’m slightly guessing – the context from the tweet she was replying to is missing.)
Luna’s birthday is 13th February.
Uncle Vernon loves Top Gear and signed the petition for Clarkson’s reinstatement. But when asked if Vernon would make a good host, she said “His total lack of charm or charisma might have prevented it becoming a global franchise”. He would vote for Brexit.
Hagrid couldn’t produce a Patronus.
James S Potter (Harry’s son) was sorted into Gryffindor. Teddy Lupin was sorted into Hufflepuff, and eventually became Head Boy. (tweet) Teddy was only appeared at Platform 9 3/4 the following year so he could say goodbye to Victoire.
Ron is not a time-travelling Dumbledore. Nor is Draco a werewolf, or Snape a vampire. Dumbledore as Death, however, is "a beautiful theory which fits". Dumbledore is not Jeremy Corbyn. (She gets asked this one a lot.)
Rowling finds it strangely upsetting that anyone would believe Fawkes is Dumbledore's Hurcrux. He isn't, and the theory makes no sense if you've "read and understood the books".
Sirius’s birthday is 3rd November.
Draco Malfoy was born on June 5th, 1980. "Girls are misguided to fancy him."
Why Harry named his kid after Snape (aka "Snape: Good, Evil or What?"):
"Snape died for Harry out of love for Lily. Harry paid him tribute in forgiveness and gratitude.¹" (Forgiveness for when "Snape projected his hatred and jealousy of James onto Harry².")
"There's a whole essay in why Harry gave his son Snape's name, but the decision goes to the heart of who Harry was, post-war.³
"Snape is all grey. You can't make him a saint: he was vindictive and bullying.⁴ You can't make him a devil: he died to save the wizarding world.⁵ In honouring Snape, Harry hoped in his heart that he too would be forgiven. The deaths at the Battle of Hogwarts would haunt Harry forever.⁶
"No, not a rant; I'm thoughtful, not upset! Snape deserves both admiration and disapprobation, like most of us.⁷
"Snape was a bully who loved the goodness he sensed in Lily without being able to emulate her. That was his tragedy.⁸ Snape didn't die for 'ideals'. He died in an attempt to expiate his own guilt. He could have broken cover at any time to save himself⁹ but he chose not to tell Voldemort that the latter was making a fatal error in targeting Harry. Snape's silence ensured Harry's victory.¹⁰ He stood to gain nothing personally but the triumph of the cause Lily had believed in. He was trying to do right.¹¹"
Snape is "the big hero/bully. He really was the best/worst".
Why was Wormtail in Gryffindor? "'I sometimes think we Sort too soon.' He travelled further and further from who he could have been."
Voldemort was "nowhere near as bad" as American businessman Donald Trump.
Canon Hermione has "brown eyes, frizzy hair and is very clever, but white skin was never specified". (Though this does contradict the way that she was described in book 6, and the way that Rowling always drew her.)
Hedwig's death was symbolism to death of childhood.
Dobby's birthday is on June 28th, because that's Rowling's sister's brithday, who loves the character.
William the Pukwudgie's voice sounds like Tom Waits.
Dean Thomas was called Gary in the original draft of Philosopher's Stone, but Jo forgot this until being reminded with a picture.
Grimmauld Place was acquired by a Black ancestor, who liked the house and “persuaded” the resident Muggles to leave.
The Salem Witches’ Institute (first mentioned in Goblet of Fire) was long believed to be the American school of magic – in fact, it’s just a joke about the Womens’ Institute.
The name of the American school (now known to be Ilvermorny) is of “immigrant origin”. “Indigenous magic was important in the founding of the school”, but she declined to say which tribes, to avoid giving away the location.
Despite being located in Uganda, Uagadou "takes students from all over Africa".
There is information on other schools (which Pottermore has yet to release) for Wizards in Australia and Canada. Wizards from Coatbridge attend Hogwarts.
The American Auror office is NOT called 'United States of America Department of Magical Defense'.
Because of it's size, North America has "more than one great wandmaker and all have different specialities"
Flourish and Blotts, the Diagon Alley bookstore, is “about halfway down Diagon Alley on the left hand side”
Gringotts will change muggle money to galleons.
Albania didn't know that Voldemort was hiding there.
Why wasn’t the soul fragment in Harry destroyed in Chamber of Secrets? Because it has to be “destroyed BEYOND REPAIR, so Harry would need to have DIED”.
With the ring, the cracked stone was irreparable, but the magic of the resurrection stone survived. Only Dumbledore could have destroyed the horcrux but not the original charm.
What cause a Patronus to change? “If it's eternal love, unchanging - part of you forever.”
Muggle-borns come through "recessive genes".
Divination is "a very imprecise branch of magic", which Rowling does not believe in, attributing it to "pure coincidence" instead.
Magic was involved in planning Bill and Fleur's wedding.
"Nearly all wizards use wands, which makes magic easier to channel. Wandless magic is sophisticated and takes more talent.¹ Wands and brooms (and flying cars) are tools that channel magic. The most gifted can dispense with them.² However, there's a cultural tradition of using wands and broomless flight is (as you might imagine) very risky
Most wizards produce more precise magic by using the correct wand, which is why they've been widely adopted.⁴ As children, wizards often produce accidental magic when they feel strong emotion. Wands help control and channel this power.⁵ The wizards deny the right to bear wands to other categories of magical being. Some think that unfair.⁶"
A duel between wand magic and wandless magic depends entirely on the individual. "A Goyle with a wand will lose to a Dumbledore without one. Most would choose wands to duel."
Mythical creature Patronuses are rare.
There is a distance limit in Apparition, and Inter-continental Apparition is "very dangerous" due to splinching. There are also Magical Customs.
This is a play happening in London, announced on Twitter. It will not be a movie.
It's not a prequel. (She says this a lot.) The story actually takes place 19 years later.
She considers it canon, although the script was written by Jack Thorne, not her. (Jack Thorne was the only writer she "wanted near the Cursed Child".
It would “give away a huge amount” to tell us who the cursed child is, but it isn't Voldemort.
The idea originated from Jack Thorne, John Tiffany and Sonia Friedman, and wasn't the first offer Rowling had received to extend Harry's story
"Due to the epic nature of the story", the play is in two parts.
The actors for Harry, Ron, and Hermione were Rowling's first choices, though she was in charge of casting.
Noma Dumezweni, who plays Hermione, is a special woman and the best actress they found. The fact that she is black doesn't matter, "because this is a play, not the 8th [sic] movie."
The script will be published in book form, but it won't be a novel. (Or a prequel.)
The play will come to other countries as well as tour.
The Cursed Child will make you cry (unless you're dead), because that is a writer's job.
Rowling is a Thunderbird and an INFJ. Her Patronus is a Pine marten Heron.
Rowling's family consists of "2 Hufflepuffs, 2 Gryffindors and 1 Slytherin", her literary agent, Neil Blair is also a Hufflepuff.
If at Hogwarts, Jo would get detention for being "too chicken to get on a broomstick."
JK Rowling had pinned her first rejection letter to her wall because it "gave me something in common with all my favorite writers!". No changes were made to the manuscript until she got an editor.
After Harry, Jo's favorite character is Dumbledore.
Her favorite chapter is Chapter 34 Deathly Hallows 'The Forest Again', which made her bawl, as "it was the culmination of 17 years' work and the most cathartic piece of writing of my life.". Her manuscript was tear stained.
She never saw "Magic Beyond Words", (the biopic about her), and therefore can not comment on it's accuracy. This is because she doesn't "want to watch somebody else's vague idea of what happened".
JK Rowling most wanted magic during the closing of the Brexit vote.
She wont run for Parliament, because she likes writing books, and because people only follow her for 'wizard jokes'.
She has nightmares about forgetting her books when talking to fans.
The first two Harry Potter books were handwritten and then typed on a 10-year-old typewriter. No MacBook Air
Jo "definitely ain't Voldemort", but she is Satan for killing Sirius, and Fred.
J.K Rowling has never turned in a manuscript which wasn't tea stained.
Rowling does not think that Richard Carters's wands are real.
"As many of you have now realised, the Pottermore Patronus Test is finally live! I took the Pottermore test (which I wrote) ages ago when it was a work in progress and got a pine marten Patronus. I was happy, because my fondness for weaselly creatures is well documented. However, when we finalised the Pottermore test last week I took it again and found that it had changed (which, as we know, can happen). My new Patronus has personal associations and I like it even better so as far as I'm concerned, the Pottermore test works! Here's my Patronus" It's a Heron.
Rowling on other Patronuses:
Rat: "Clever, resourceful and (according to the Chinese) lucky!"
Mole: "You got the Lord of the underworld who brings light to darkness. Of course it's awesome."
Peacock: "The peacock is a symbol of immortality in certain cultures and nothing to do with vanity. Just saying."
Vole: "I love them!"
Adder: "That's what you need to fight your fears: face them!"
Osprey: "You cast it, you keep it. (What's wrong with ospreys?) x"
Runespoor: Does it make me evil? "No, it makes you fascinating."
The comprehensive (state school) that Rowling attended also had four houses. She was in Armstrong.
The gems in the Hufflepuff hourglass are diamonds.
The Bulgarians are “outstanding at Quidditch”.
The Ministry of Magic covers the costs of magical education, at least for Hogwarts students.
The Magical Congress of the USA is a single body, unlike the two-part real-world Congress.
The equivalent of the United Nations is the International Confederation of Wizards.
If Crookshanks and Mrs. Norris were to have a fight, Crookshanks’s Kneazle ancestry would give him the edge.
"Not all Slytherins think they're racially superior. But all those who do are Slytherins." Rowling recommends Slytherins to curse anyone who makes fun of them.
Gryffindors do occasionally get anxious.
A group of Puffskeins or Pygmy Puffs is called a poffle.
In Rowling's fictional Wizarding World, skin-walkers did not exist, but were just "a legend created by No-Majes to demonise wizards".
Handwritten (suicidal-prevention-tattoo-ready) "Expecto Patronum"
Pottermore will get an Ilvermorny sorting quiz and a Patronus sorting quiz. "If you need a test to find out what your boggart would be you're either fearless or addicted to quizzes."
Quidditch is easier to understand than pointsrace cycling Olympics.
There were "many, many, requests" to make the previously free digital Pottermore writings available in a digital format that cost money. She'll still complain when people fall for the false advertising of this being new content.
This answer will focus just on the tweets related to the Fantastic Beasts movie. Up-to-date as of the end of 2016.
This is the new film series based on the book of the same name, due for release in November 2016. The film series is a prequel (She says this a few times.) to Harry Potter.
It will be a trilogy five films. (No more, No less.)
The five films have a "natural arc", spanning from 1926 until 1945. "When you realise what story we're really telling, you'll understand that it can't possibly fit in one movie". "There's just too much story"
The movies are about "good versus evil" and Grindelwald's view is supposed to make sense.
Later exciting installments will introduce new characters, including some who aren't white.
The Second installment will be set in Paris, but not immediately after the first one finishes. You'll get to see more of Tina 'being badass'. Queenie will also return, and Newt will remain the main character. We will find out who Leta Lestrange is and why Newt was allowed to keep his wand.
Newt Scamander is a Hufflepuff and is British. Eddie Reyhman is "undoubtedly" the perfect actor to play him and brings the character to life exactly as Jo imagined him.
The first line is “Newt Scamander only meant to stay in New York for a few hours”. Initially posted as an anagram for her followers to unscramble.
Newt will meet characters from the American school of magic. It sounds like the American school also has a house system, and she knows where those characters fit. "There is no equivalence between Hogwarts and Ilvermorny houses." Tina is Thunderbird, Queenie is Pukwudgie, Seraphina is Horned Serpent, and Jacob would have been a Wampus.
There’s a character with “loads of scars”.
There are two characters – Portentina (shortened to to Tina by her friends and family) and her younger sister Queenie – who have the surname Goldstein and are distantly related to Anthony Goldstein in Harry’s year. Tina, who is "perfectly" played by Katherine Waterston, has had a hard life, (and has a "particular place" in Jo's heart). "Everyone's in love with Queenie."
Queenie is a naturally-born Legilimens, (as oppose to Snape who had to train), but is not infallible. She was unable to detect Grindelwald due to Occlumency.
The Jacob/Queenie ship is called Jakweenie, and the Newt/Tina ship is called Newtina.
The most exiting part involves spoilers.
The whole script was written and finished by Rowling. (She isn't merely approving other peoples writing.) Therefore, these movies should be considered canon despite any divergences with the books.
The published version of the screenplay is dedicated to Rowling's late father-in-law, Gordon Murray - "a veterinarian and one of the people I've loved most in my life."
"Albus Dumbledore is fond of Newt Scamander for the same reasons that I am fond of Newt Scamander." However, at the time of Newt's expulsion Dumbledore was just a young teacher who didn't have the power to revoke it.
Newt only deals in "lovable monsters" and is "deeply opposed to creature trafficking" (which is prohibited by Ministry Ordination 297b). Nevertheless, Newt used Muggle customs so he could illegally smuggle magical creatures. He doesn't encourage visitors to his case.
Newt did not use a portkey when traveling to New York because of the effect it would have had on the contents of his case.
The "little alpaca like creature with giant eyes" was a mooncalf.
An Obscurus is not a baby dementor, but Rowling loves the thought.
Grindelwald is a seer, and was lying about the vagueness of his vision.
The scarf Newt was wearing at the end of the film was a Hufflepuff scarf.
Frank the Thunderbird made it back to Arizona.
Jo will come to New York to promote the movie.
The upcoming expanded edition of the original book will feature a longer foreword from Newt Scammander. Although it will have six new entries, none of them will be on Obscuruses because "an Obscurus isn't a creature".
