Over the course of the show's run its producers, Benioff and Weiss, have received a great deal of grief over the changes they have made to the story. Justified as this may be, the fault does not lie entirely with them. Ever since Martin began writing his grand epic he has been making changes as he went along. The story as it now exists bears little resemblance to his original conception. This is proven by the sample he sent to his publishers when he was working on the original A Game of Thrones. I have long waited for youtubers to create a video covering all the broken plot lines and suggested story arcs which Martin has in his story. Unfortunately, nobody appears interested in making such a video. So on this page I am going to try to list at least some of what I think Martin had intended to put in his story. There are surely more that I haven't noticed.
1) Tyrion, the Secret Targaryen - Obviously I have to cover this one. I think Martin definitely did intend this to be a part of the story to begin with. He originally intended for Tyrion and Jon to be in a love triangle with Arya. His description, as very many people love to point out, bears far too many Targaryen characteristics to be a coincidence. The most likely explanation for this is that Martin originally intended for both Jon and Tyrion to be Targaryens. Both would join Daenerys and they would become dragonriders. But the two would have a falling out over Arya. They fight a dragon duel with Tyrion getting the worst of it. His dragon would be killed. Tyrion would then betray Dany and join his brother, Jaime. Jaime was originally intended to be the main villain.
Why Martin changed this is probably because he found Tyrion's relationship with his father Tywin more interesting. A Targaryen background for him would actually detract from it, as Alt-Shift X says in their video on it. So I am now certain that Martin intends for Tyrion's appearance to be pure coincidence.
2) Magic - This one is more ambiguous. I suspect Martin has gone back and forth regarding how much magic he actually wants in the story quite a bit. One thing I do think is that he was going to have a more Dungeon&Dragons feel to the story than it has. Martin was an avid gamer at one time and the hints of the game origin for his world are clear to see. What he probably wanted was that both Tyrion and Daenerys would be magic-users, ie: They would actually cast spells of some kind. For centuries it has been a common folk-tale that witches and warlocks have identifying marks on their bodies caused by their use of magic. Tyrion's mismatched eyes were likely intended to signify that he was someone with magic power. Much like Shiera Seastar. His acrobatic abilities, which were much more prominent early on than later, were also likely to be more Jedi-esk. Quaithe was probably originally intended to be Dany's teacher. She was going to be a regular character in the story, rather than doing cameos. Martin probably dropped all this because it caused some characters, namely Daenerys, to be over-powered.
3) Arya's Training - In the original configuration of the books it was only going to be a trilogy. In Arya's case that means that she was never going to go to Braavos. Braavos was probably not going to appear at all. Instead, Jaqen H'ghar was going to be her travelling companion for awhile, whether with the Hound or prior to her joining him. Jaqen would teach her all his skills during their travels. The Hound too was also going to be more her swordmaster. Have no doubt that Arya was and is intended to become the 'super ninja' she becomes in the show. This has been telegraphed from the beginning. Its how she gets there that has changed.
4) Dany's Visions - The meaning of Dany's visions has also been changed. Upon making the pages on Dany's visions I noticed something that had escaped me before. The three visions belonging to Bride of Fire are all the same as the Three Mounts with the exception of Euron. The answer to the puzzle is in the original trilogy format of the books. In that form Hizdahr zo Loraq hadn't even been conceived of. Martin likely had planned that Dany would marry Euron and he would be the Mount to Dread. The Fire for Death was probably going to be Dany burning the Iron Fleet. Dany's rescue by Arya was always in the cards.
5) Dany's Visions 2 - In keeping with the previous point, another thing I noticed was Slayer of Lies. All three in the original trilogy would have been Dany's main opponents. Today the idea that Dany would fight Stannis is almost an absurdity, if for no other reason than because the chance of Stannis still being alive when Dany reaches Westeros is near on impossible. The original plan was likely that Stannis and Faegon would subdivide the kingdom, Stannis controlling the North with Faegon conquering everything south of Kings Landing. How the third vision fits in is still not clear to me, but I think it was probably something Qyburn was going to do. Mayhaps an undead dragon brought to life through necromancy. Qyburn would have done this for Jaime, who was the main villain back then. The vision itself is the beast bursting out of the Red Keep. In that case the lie was the dragon itself, which wasn't a real dragon.
6) Dany's Visions 3 - Continuing, the Treason for Gold was going to be Jorah betraying Dany as so many people assume. Only in this case he would have betrayed her to Euron, likely motivated by her rejection of him. He would sell her out, probably her plan to escape him, and this would lead to her burning him and the Iron Fleet.
7) The Deaths of Jaime and Cersei - It is set out in the very first book, A Game of Thrones, that Jaime and Cersei would die together. This was based on the original setup of Jaime as primary villain. Cersei was designated as female underling. That was before Martin had created the character of Brienne. Just as Martin preferred the interplay between Tywin and Tyrion, he also preferred the redemption arc between Jaime and Brienne. It was because Brienne changed the dynamic between the siblings which caused Martin to promote Cersei to primary villain. One also can't help but notice how much more prominent Cersei plays in the story even at the beginning.
8) Shaggydog and Rickon - Rickon was almost certainly meant to remain with Bran until the end. His end. It is likely he was meant as a moral warning regarding the overuse of magic. Rickon was going to lose himself inside Shaggydog and turn feral. He would then kill Jojen, forcing the others to kill him. Martin most likely changed this because it was too much on the nose. And he wanted to add unicorns to the story.
9) Arya's death, or not death - In the original incarnation Arya would have gone north of the Wall with Catelyn. Catelyn was going to be killed by the Others and she would rise as a wight. This is very important to Arya's story. Something most readers don't seem to get. Arya having to kill her own mother is meant to force her to question the rightfulness of killing. It is a deliberate allusion to Gandalf's words to Frodo - "Many that live deserve death. And some that die deserve life. Can you give it to them? Then do not be too eager to deal out death in judgement. For even the very wise cannot see all ends." Wight Catelyn was transformed into Lady Stoneheart in the final version. This too is meant to force Arya to face her willingness to kill. In this case she will be unwilling to kill her mother and will be killed herself instead. Her undead mother will then face her own willingness to deal out death and change her mind.
10) Quaithe's parade - Thanks to the Order of the Green Hand I have been reminded of another broken plot, this one more recent. Quaithe warns Dany of multiple people who are seeking her out, which are listed in the article on Quaithe's visions. When Martin first conceived of this vision is unknown, but like the Valonqar prophecy and the visions in the House of the Undying, this is likely to be one of the pieces that served as inspiration for the story. It feels like something Martin was using as a guidepost, directing the narrative. But as with so many things its meaning was changed. Likely this was because it upset the pacing. All the people mentioned were probably meant originally to go to Meereen before continuing on their separate courses. But this would require more time than Martin wanted to take. Also, having Tyrion persuade Faegon to go to Westeros gave Tyrion something to do.
Addendum for 1, 4, 5, and 6) It has come to my notice that I may not have been entirely clear regarding the different meanings of Dany's visions. So I have spelled them out.
A) Daughter of Death - all involve three male relatives who have to die for Daenerys to become the Queen. Not just to clear the way for her promotion, but because their deaths lead directly to actions Dany has to take. Or in Rhaegar's case, providing her with her future (hubby).
B) Slayer of Lies - all are about the original three enemies Dany would have to fight to obtain the throne: Stannis in the North (the lie is he's Azor Ahai), Faegon in the south (that he's Rhaegar's son), and Jaime in Kings Landing (That Jaime has his own dragon. It would probably have been an undead Viserion. The tower in the vision is the Tower of the Hand).
C) Bride of Fire - this one is the most alike in character to the end meaning. All three were originally meant to be the men Dany would marry and later cause to be burned. The first is obviously Khal Drogo, who was actually supposed to be a villain to start. He remains the Mount to Bed. The original Treason for Blood was his killing her brother, Viserys. The Fire for Life was actually her brother's pyre and not Drogo's. The second, as stated above, is Euron Greyjoy, the Mount to Dread. Jorah the Treason for Gold. And Dany burning the Iron Fleet, with an assist from Arya, along with Euron and Jorah the Fire for Death. The third remains Jon Snow, the Mount to Love. But he doesn't get torched the way the other two do. There are two possible options that Martin probably considered:
1) The first version was that Dany would join up with Jon when he was still the Lord Commander. She, suspecting his true parentage, betrays him to his Night's Watch brothers who then murder him (Treason for Love.) She then lights his pyre causing him to be resurrected (Fire for Love.) In this version there was more magic in the Targaryens to start with. They had a far greater affinity with fire. It is the fire and not Melisandre which brings Jon back to life. This is what was actually meant by Dany's comment that Verserys was not a dragon. Pure blooded Targaryens originally were meant to be fire-proof and obtain power from fire. She would then have married him (Mount to Love.)
2) The later version was Dany would cause a feud between Tyrion and Jon. Likely this involved her trying to arrange a marriage between Tyrion and Arya. Jon would object, causing the two men to go at it with their dragons. This is the original Fire for Love. After Tyrion loses to Jon he turns his back on Dany and joins Jaime. This was going to be the Treason for Love.
I have no idea how much of this is going to appear in the final books, but I suspect Martin will try to put as much into them as possible.
This final topic is not a broken plot per-say. Rather, this is in answer to the insistence I have heard from many Youtubers that the ending to the show is fundamentally what it will be in the books. Not to be too blunt, but poppy-cock. George has been quoted as saying Benioff&Weiss got an ending, not THE ending. That statement could just as easily mean that they got the ending for a single character right as meaning that they got the end of the story right.
As I have already laid out within the articles on this site, there is not a chance that the ending presented on the show will be the ending in the books. I cannot promise that the ending I have given is the correct one. Only that the balance of probabilities, based on the evidence in the text, leads to this conclusion. However, alternatives are possible. As Quinn has noted, Martin takes a great deal of inspiration from Dune. And this suggests to me a more Dune-esk ending. I have to stress that this is not the ending I believe George will ultimately use, otherwise I would have used it in my book summaries. What it is however is far more likely than the ending Benioff&Weiss gave us.
What leads to this ending is the apparent difficulty people have in understanding what 'bitter-sweet' means. Bitter-sweet, in the classical literary sense, means that the protagonist obtains their desired goals, but the cost of doing so renders the achievement meaningless or Pyrrhic. In this ending the conclusion for most of the characters is the same as I have set down in my summaries. The difference regards three characters: Daenerys, Jon, and Arya.
Most of the story remains the same. The differences begin with Dany declaring herself Queen of Westeros without marrying Jon. She does acknowledge him as her nephew and heir. And they do become lovers. They succeed in defeating the Others, but a combination of the loss of all her dragons with a difficult labor destroys Dany's mind. Jon becomes King and marries Arya. But then he disappears with Dany, never to be seen again. Arya is left as Queen of Westeros and having to raise Jon's son on her own.
Thus Dany achieves her goal of restoring her family to the Iron Throne, but loses everything she values most; her dragons as well as her mind. Jon receives the recognition he craves and saves the world from the Others. But he loses the woman he loves and the loving family he wants. Arya obtains her revenge on Cersei and marries Jon. It is never explicitly stated in the text, but there are hints that this is one of her primary goals. But she ends up losing him and is forced to live the very life she doesn't want.
As an additional note, Bran's ultimate fate might also be affected. Bran, who has lost his original body might choose to inhabit the baby. Jon's son, thanks to the same medical problem that wrecks Dany's mind, will also destroy the boy's. It is very possible that Bran will take the opportunity to take the boy's body for his own. Nobody else will know that he does this. Kinda like Professor X.
This strikes me as the closest ending to Martin's that anyone has suggested. The question is: is it still his ending? If it is than there is no chance Martin will ever finish his books. This ending simply does not match up to what he has written since he's started. If he insists on using this ending than we are unlikely to ever get an ending unless a relative of his finishes the novels after his demise. See: Brian Herbert.
The ending I give in my hypothetical summaries are the ones I think are most likely to actually be used assuming he manages to finish them.