Some literature has had issues with Broken Base since before fans were even called "fans".
The ending of the Harry Potter series pretty much split the base in two, especially the epilogue, which was either an appropriate coda that closed the circle while showing that life would go on, or a piece of rubbish that shamelessly abused the clichés of the series and was the worst thing in all seven books.
One of the key factors in this was the fandom, who are famously argumentative (particularly Harry/Hermione versus Ron/Hermione). That said, given the size of Harry Potter fandom, pretty much any strong opinion about any ships or characters could cause an argument in the wrong forum.
Also, some have actually accused Rowling of homophobia, given that of the Loads and Loads of Characters, none was stated to be gay. Accordingly, the final scene of Half-Blood Prince was bashed for "pairing everyone up in neat little heterosexual rows". When she outed Dumbledore as gay, she was criticized for being too cowardly to put it in the books, though there was some arguable basis for that interpretation in the seventh book.
The outing created two very distinct camps - Dumbledore's Not Gay, She Made That Up to Make Herself Feel Better vs. It Was Obvious Or Maybe It Wasn't, But It Didn't Matter Then (Purple Velvet Suit people!)
Are the books for kids or for teenagers/adults? And if you go by common knowledge (that the story "grows" with the original readers, so the earlier books are more kid-appropriate than the later ones), with which book do you draw the line? Azkaban? Goblet? Phoenix? And should the movies/marketing cater to the new kid fans, or to the now-grown original fanbase? (Simply rating Goblet PG-13 caused a huge ruckus)
The various tidbits of information J.K. Rowling has dispensed during various interviews before and after the publication of the last book has caused a rift in the Harry Potter fandom between fans who take those tidbits as the Word of God and those who say that if Rowling wants to make something official, she should write another book, because in their opinion, unless its published in a book, it's not official.
One of the biggest broken bases of all. Reader's reactions to Snapes's last words to Harry "look at me" (with Lily's eyes) followed by the revelation of Snape's entire relationship with Lily and his reaction to her death. Depending on who you ask it's either a tragic, romantic Tear Jerker or deeply creepy and disturbing.
The fandom for A Series of Unfortunate Events has experienced some division over The Film of the Book, which condensed the plot of the first three books with a vague approximation of the Ancient Conspiracy material from later ones, and over the vague ending of the actual book series (some thought it was nicely in-keeping with the developing themes of unanswerable questions, others had hoped for some more tangible resolution).
Not to mention the slash fandom v. non-slash fandom. All the pretty elves and men! vs. Tolkien would never have approved, and you are being untrue to the spirit of the books by slashing anyone! I'm pretty sure the two sides don't even talk to each other. They even have two huge completely separate fandom archives. Stories of Arda is a family-friendly, strictly gen and het archive with stringent posting guidelines which explicitly declare the movies uncanonical. The very not worksafe Library of Moria has only two guidelines - no het and no gen.
And let's not overlook the Balrog wing debate.
Twilight has a nearly equal amount of Jacob/Bella and Edward/Bella fandom, causing massive Ship-to-Ship Combat. This cartoon pretty much sums it up, except for not having a "Team Couldn't Care Less" choice.
The base seems to have split even wider with the release of Breaking Dawn. The hardcore Twilight fans still say it's the best thing since smoked cheese, while others (including those who haven't just read the series for its Guilty Pleasures value) are still trying to repair the holes in their walls after reading through some of the bizarre and improbable plot twists.
One could also argue that the largest split occurred when the series was popularized by the Twilight movie. It basically split avid readers (or people who had previously not heard of the series at all) into people who pretended to always hate it because of how popular it made the books, people who like the books but hate the movies, and people who have Edward Cullen bedspreads, with few neutral positions otherwise.
The Hatedom, particularly the ones with the Pass the Popcorn attitude towards the fans, can't wait until the movie ofBreaking Dawn comes out, purely so they can see what the fans do then.
Since late 2004, The Phantom of the Opera fanbase has been divided into people who loved the movie of the musical and people who despised it, with a side order of people who dislike the musical period and prefer to stick with the original novel.
Matters worsened with the sequel to the musical, Love Never Dies. There is absolutely no middle ground on that show and what it does to the established characters, and it doesn't help that the Really Useful Group seems determined to provide Flame Bait whenever possible.
The Wheel of Time fanbase often argues over whether the series jumped the shark somewhere between Books 5 and 10, with die-hards claiming that the series never jumped at all whilst the majority seem to at least agree that Book 10 is absolutely horrendous. There is then the question of whether Book 11 successfully repaired the damage or was a case of too little, too late. Then are the fans divided over whether Brandon Sanderson finishing Book 12 after Robert Jordan's death is a good thing or not. There are also the fans who argue that Robert Jordan is a master of depicting male-female relationships, whilst others claim that all his couples, even the older ones, behave like 13-year-olds and loathe the relationships whilst praising the worldbuilding and magic system. There is also a group of fans who anxiously still want to know who killed Asmodean (a minor Heel-Face Turn villain killed by unidentified means at the end of Book 5), whilst other fans see it as a pointless mystery of no import that does nothing other than spark arguments. In short, Wheel of Time message boards are like minefields waiting to explode if you say the wrong thing at the wrong time.
Not to mention the split between fantasy fans who hate TWOT with a firey passion and those defending it at LOTR's equivalent, or better.
Solved. The epilogue of The Towers of Midnight specifically states that Graendal had 'Three Chosen, destroyed by her actions.' So assuming Mesaana and Aran'gar are killed by Graendal, the last Chosen to be killed would be Asmoedean, since most of the Chosen are explicitly killed by either Rand or balefire.
The Anita Blake series fandom is fiercely split between fans of the earlier books who view much of what has transpired since book ten, Narcissus in Chains, as little more than a series of sadomasochistic fanfics featuring similar characters to those present in the earlier books and the 'Troo' fans, many of whom started reading the series in the middle and loyally and often vigorously defend the literary skill of the author and the direction she has taken the series.
The phrases "Warrior Cats fandom" and "majority opinion" simply aren't compatible. If you try asking which series is the best on a forum, you won't get the same answer from everybody. Some parts of the fandom think anything outside of the Original Series is crap, but can't agree on what "sucks" more, or at which point everything started "sucking". This is divided even further by the fact that for both of most recent series people can't reach a consensus over whether the first three books sucked and the last three were great, or the first three were great and the last three sucked. Sunrise has also divided fans into a group who think it was a literary insult, and a group who think it was one of the greatest books in the entire series. Then there are the people who like all the books.
It is simply physically impossible to find another person in the Warrior Cats fandom who likes and dislikes the same characters as you. Don't even try. Almost all the main characters are prone to having several lovers and fandom, most notably being Ashfur, who has divided the fandom into people who believe his attempts at revenge against Squirrelflight were completely unjustifiable and that he doesn't deserve an ounce of sympathy, and people who turn all his problems and losses Up to Eleven and believe that Squirrelflight was manipulating and trying to hurt him purposefully. A middle ground would be that while an attempt at murder is always wrong, the amount of emotional pain and trauma Ashfur felt from being rejected (especially since he had been under the impression that she loved him back right until she dumped him) should warrant sympathy and understanding for what he tried to do. But there, apparently, is no such thing as a middle ground.
The author also enjoys writing spin-offs to give most of the villains sympathetic backstories. The only problem with this is several fans completely misinterpreting them and believing that the Big Bads are genuinely good (see Rise of Scourge). This causes disagreements between these fans, and the fans who like them being evil.
Shipping. It's like the series was written to create shipping wars. There are no less than three characters with three canon pairings for each of them (Daisy doesn't count, because no one likes her and all shippings involving her have died by now).
One notable example was Lionblaze - Cinderheart, who he'd most recently had feelings for? Heathertail, who he was friends with as kits? Icecloud, a pairing that fans like?
Old Names vs New Names. Do you think the old names are too plain? Do you think the new ones are too stupid?
Ivypool and Dovewing. Apparently, if you love one of them, it is absolutely mandatory that you hate the other with a burning passion.
Although not to the same degree, there is a bit of this happening with other characters. For example, if you love Leafpool, you have to hate Nightcloud (or vice versa). If you love Firestar, you have to hate Scourge (or vice versa). If you love Ashfur, you have to hate Squirrelflight (or you just hate Ashfur regardless of your character preferences).
According to the author, the series is written to avoid any straightforward answers in terms of right or wrong, leading to a lot of disagreements over most major characters. Discussing who is right and who is wrong can sometimes reach Mind Screw levels.
It sounds like you might say that it's almost like... herding cats.
For a period in the 1990s, when Doctor Who had no new TV content to provoke fan infighting, a lot of fan arguments circulated around the Doctor Who Expanded Universe book ranges and in particular the categories of 'trad' (books which attempted to mimic the old series as close as possible, just in book form) vs. 'rad' (books which attempted to tell stories 'deeper and broader than the small screen', to quote the tagline of one range of them). Since the new series came along and stole the Expanded Universe's thunder somewhat, these arguments have tended to die away.
A related but distinct split was framed by Doctor Who New Adventures writer Gareth Roberts as "guns" vs "frocks"; "guns" are Serious Science Fiction, where the heroes have to use violence to win and the Doctor has to, at the very least, condone it and "frocks" are lighthearted stories where the Doctor saves the day by being clever and the villains are Hoist By Their Own Petard. Sometimes "rad" and "gun" were considered synonymous (suggesting Grim Dark stories the TV series couldn't possibly have done) as were "trad" and "frock" (Roberts's own "in the style of Season 17" books), but you could also have rad frocks (such as Sky Pirates!, a joke book which casually suggests the Doctor is a Humanoid Abomination) and trad guns (such as Warmonger, which deftly recreates the already fairly Grim Dark feel of Season 22).
George R. R. Martin: Has his constant postponing of The Winds of Winter and endless secondary projects mean he's lost interest in his own series, or should his fans stop bitching and let him write his books at his own pace?
There's also the split between those who think the post-A Storm of Swords books are solid installments full of character development and setting the stage for the second half of the series, or meandering, padded messes that prove GRRM has bitten off more than he can chew.
The ending of Trudi Canavan's Black Magician Trilogy has sharply divided fans, those who despise the ending being the most vocal. Many fanfiction pretend the ending never happened and discussions on pretty much anything regarding the series are prone to derail into angry author bashing.
The Xanth fandom can be split pretty cleanly into two parts: Those who love the Hurricane of Puns and keep coming back for more and those who gave up on the series because the puns practically took over the series. A good chunk of the latter cite the introduction of Ptero as the last straw.
The Wicked fandom is more or less broken into three parts: The book fans, the musical fans, and the ones that enjoy both. Within the musical fans there are the fans that are dedicated to one set of actresses, the most common being Idina and Kristin; there are even some fans who don't want to watch The Movie if those two aren't cast as Elphaba and Glinda. The fandom as a whole is divided on whether the book, musical, or source material are the best.
A big Base Breaker is the shippings. The main one is Glinda/Elphaba (Gelphie) vs Fiyero/Elphaba (Fiyeraba); it helps that both shippings have Word of God and canon on their side in both the musical and book.
The Maximum Ride series. Oh, boy. When the fourth book came out, it divided the fanbase. Bring it up and it drives fans into an all-out war. Some really liked it, but others were driven completely up the wall at the plot shift from "bird kids running from Mad Scientists and wolf monsters" to "bird kids save the world from global warming".
Fans of the Cthulhu Mythos are split between those who consider August Derleth's application of good-vs-evil themes to Lovecraft's amoral Cosmic Horror Story Verse to be sacrilege, and those who have no problem with it as long as it makes for a good story.
So far, the split is small, but the Dresden Files novels are losing some fans since book 12, Changes. Book 13, Ghost Story, increased the numbers, as did Cold Days, book 14. Some fans say the series ended with book 12.