Author Existence Failure: Something that fans continually fear, especially since Martin is well into his sixties and it took him nearly six years to complete A Dance with Dragons. What also doesn't help is that he has gone on record to state that if he does die, he won't allow another author to finish his work. Fortunately, he already knows how the series as a whole will end, and has told the producers of the Game of Thrones TV series several major plot points in advance (though they've been very different about how they've been incorporating those elements).
Development Gag: Near the end of A Feast for Crows Littlefinger describes how quickly Cersei is destroying herself and how vexing it is for his plans, as he had hoped to have four or five quiet years before the next conflict ensues, which alludes to the Timeskip that Martin had previously planned between the third and fourth books.
Development Hell: A Dance With Dragons was "forthcoming" in one way or another starting in 2004, but was published at last on July 12th, 2011. Time will only tell if The Winds of Winter and A Dream of Spring will eventually fall under this trope, though Martin said in a 2014 interview with The BBC on an unrelated matternote An independent theatre Martin co-owns was one of several that decided to show The Interview after the Sony hacking mess. that he is still working on them.
Based on correspondence with GRRM, who refused to confirm that Rhaegar's son Aegon was killed during the Sack of King's Landing, some fans began to believe that it was a decoy that the Mountain snatched from Elia's hands and smashed against a wall. Guess who shows up in Tyrion's chapters?
Also, in DVD Commentary for the TV show, GRRM confirmed that the undergaoler "Rugen" is one of Varys's disguises.
Fans had speculated for decades that Jon Snow is Rhaegar Targaryen and Lyanna Stark's son. This is confirmed in the Game of Thrones season 6 finale. Since it's public knowledge that the identity of Jon Snow's mother was the piece of information that got series showrunners David Benioff and Dan Weiss the job adapting the show in the first place, this has in turn all but confirmed it for the books as well.
Saved from Development Hell: A Feast for Crows and A Dance with Dragons both took years to write, causing some fan complaints to reach a fever-pitch, but both were eventually completed.
Shrug of God: After the release fiasco that was A Dance with Dragons, Martin no longer risks giving a concrete estimate for when his next book will be finished. He has also remained frustratingly vague on whether he will wrap up the series in the next two books or if he will expand it to three or more.
One of Martin's early plans involved each chapter being a few months apart, but he discarded it for the same reason he would eventually abandon the Time Skip described below: the missing time would necessitate a large amount of exposition and flashbacks.
Martin originally planned to have a five-year Time Skip between the third and fourth books, which would have had a major effect especially on the several child and teenage characters. In the end, he wasn't able to pull it off. And ironically, there actually was a five year gap between the two books' publication. He lampshades it with one character saying (paraphrased) that he "expected five years of peace, at least, before Cersei screwed everything up."
Several chapters were edited out of A Dance With Dragons, including ones for Aeron Greyjoy and Sansa, who didn't have chapters in the finished version. Their chapters have reportedly been moved into The Winds of Winter, so we'll have to wait and see if that is the case.
In 1993, Martin wrote a three-page letter with his original pitch for what he thought would be a trilogy (A Game of Thrones, A Dance with Dragons, and The Winds of Winter). He stated that he had an overall structure worked out but that he didn't know exactly how it would pan out and expected to make changes along the way. The differences between the planned novels and the actual novels are quite vast, although some plot points were used in heavily reworked forms. In the original pitch for A Game of Thrones:
Daenerys, instead of taking Drogo's side in killing Viserys, eventually murders Drogo in revenge. While this makes her a pariah among the Dothraki, she would somehow regain their favor and eventually invade Westeros with her horde in A Dance with Dragons.
The summary of Bran's arc implies that magic is more commonplace or at least significantly different from its portrayal in the final version of the series.
Ned manages to help Catelyn and Arya escape from King's Landing to Winterfell before his execution.
Sansa marries Joffrey, has his child and chooses him over her parents and siblings, a decision she comes to regret.
Tyrion becomes close friends with both Sansa and Arya, and eventually falls in love with the latter.
Robb maims Joffrey on the battlefield, only to later die in battle.
Tyrion besieges and burns Winterfell.
Benjen is Lord Commander of the Night's Watch until Jon Snow takes the mantle.
Following Tyrion taking Winterfell, Catelyn, Bran and Arya go to the Wall for refuge. However, they are turned away due to the Watch's vow of neutrality, which bitterly estranges Bran and Jon. Arya realizes she has fallen in love with Jon. Afterwards, Catelyn and her children try to find refuge beyond the Wall, only be captured by Mance Rayder. Catelyn is later killed by an Other.
The Others have a second type of minion alongside the wights, called "neverborn". Whatever these are is not elaborated upon.
Tyrion removes Joffrey from the throne. Jaime takes the throne by killing everyone else in the line of succession and frames Tyrion for the murders, resulting in his exile. Tyrion then teams up with the Starks to remove him from power, though he and Jon have a Love Triangle regarding Arya. Arya for her part angsts over Jon until the final book "reveals his parentage".
The Wiki Rule: A Wiki Of Ice And Fire is the biggest, and can be found here. There's also A Song Of Ice And Fire Wiki, which can be found here.