Ice cream parlour owner Florean Fortescue was supposed to have a much bigger role in the book's story - he was originally supposed to be kidnapped and saved by Harry, Hermione, and Ron, then given them clues about the Elder Wand and Ravenclaw diadem. This was cut as, in Rowling's words, the sequence was "going nowhere", though it does explain why the closure of Fortescue's shop and his kidnapping receives such emphasis in Half-Blood Prince.
As Rowling wanted a Sacrificial Lion, this resulted in Lupin and Tonks getting killed off in the last book. Arthur again very nearly got killed off too. Ultimately it was Fred who was killed.
Rowling was originally going to make Helga Hufflepuff's Horcrux a cauldron, but decided that a cauldron was just too clunky to be an effective Horcrux.
Evanna Lynch revealed that Rolf Scamander (Newt's grandson and Luna's future husband) almost made it into the book and would have been the one to explain The Tale of the Three Brothers. The role was given to Luna's father instead.
A lot of material released after the last book's release (such as the trio's lives after Hogwarts) were trivia Rowling would've liked to include in the actual book.
Rowling considered giving Dudley a Muggle-born wizard child for the epilogue, but in the end decided that "no wizarding traits would ever survive contact with Uncle Vernon's DNA". Shame, that would have been a lovely little twist.
Curse of Nagini was trademarked in 2005 by WB after Rowling gave them a rough list of potential titles, suggesting that her Was Once a Man storyline that was re-worked into Fantastic Beasts was originally supposed to be introduced here.
Films
The film was intended to be a single installment just like the rest of the series. However, the creators found it too difficult to compress the book into one film due to the relative lack of extraneous subplots the others had.
John Williams wanted to return to compose the score, but a scheduling conflict prevented him from doing so.
Billy Connolly was in talks to play Xenophilius Lovegood.
Kate Winslet was the first choice for the Grey Lady, but as with Naomi Watts in the previous, they couldn't get through her agent, and Kelly Macdonald got the part instead. It's unknown whether Winslet would have said yes. This marks the second franchise Winslet narrowly missed out on (having nearly played Sauron in The Lord of the Rings), though she would eventually get to be part of a franchise with Divergent.
Crabbe would've suffered the same death he had in the book had his actor not been found with marijuana. His role as the sole casualty of the Fiendfyre is given to Goyle.
Producers tried to change Minerva's duel with Snape to happening with Harry instead. Rowling had to step in, insisting the duel was an essential part of Minerva's character.
There was serious consideration for filming the deaths of Lupin and Tonks.
A scene during the final battle was filmed where Draco would toss Harry his wand after he reveals that he's alive to Voldemort. This made it into the video game adaptation.
The epilogue had to be re-shot because the aging make-up on Daniel Radcliffe, Emma Watson, Rupert Grint, Bonnie Wright and Tom Felton didn't look good in the footage. Photos exist showing drastically different costumes and hairstyles for the actors.
The two halves of Deathly Hallows were written and filmed as one giant four-hour film. It was worked out in editing where to put the break between Part 1 and Part 2. Originally, the break was tentatively planned to occur after the Trio is captured by the Snatchers, but it got moved to after Voldemort recovers the Elder Wand. This means the battle at Malfoy Manor was originally intended as the beginning of Part 2, but instead became the end of Part 1.
, suggesting that her Was Once a Man storyline that was re-worked into Fantastic Beasts was originally supposed to be introduced here.