The fifth Cahill branch, the Madrigals, and the fact that their founder was Madeleine Cahill, make it practically impossible to discuss the first series or the ancestral Cahill family without spoiling some of the most surprising revelations in the series. Madeleine's existence isn't even revealed until near the first series' end.
A lot of the enemies as well, due to their Heel-Face Turns at the end of the first series. Sinead Starling in particular becomes a big one due to her turning out to be Vesper 3, The Mole, in the second series.
The Agent Pendergast series has Tristram and Alban, the twin sons of the title character. Since they do not appear until Two Graves, one of the later books in the series, and the twist related to them isn't brought up until roughly a quarter through it, it's impossible to bring them up without also referring to their role in the series.
Julius Grief in Alex Rider. Originally an unnamed clone of Dr. Grief who looks just like Alex from Point Blanc, he's thought to have died in the chapter he was introduced in. Nope, he was just arrested and comes Back for the Finale as a member of Scorpia.
Animorphs has Marco's mom Eva. We know very little about her past, other than that she was killed in a tragic boating accident, and her husband couldn't stop mourning her. She's also the host of Yeerk commander Visser One, who faked her death, and soon grows into one of the series' most dangerous antagonists.
Avalon: Web of Magic: The cover of Ghost Wolf depicts a human girl and two wolves running alongside her. Not coincidentally, there are only two wolf characters in the entire series who are remotely important, and one of them "died" in a previous book. Storm's appearance can't even be written off of as symbolism, courtesy of the stream of wolf spirits that are also on the cover, which- unlike Storm- aren't depicted as physical beings.
In the Warrior trilogy of BattleTech novels, Justin Xiang Allard's entire role is to be the Fake Defector who becomes the enemy spymaster to help sabotage the Capellan Confederation's efforts in the upcoming Fourth Succession War while pretending to do his best to use his knowledge as the son of the Federated Suns' resident spymaster to their advantage. This bit of information is easily found in most histories of the BT universe as well as referred back to in later fiction since these books were among the earliest written for it and the timeline has long since moved on, but acts as a major spoiler for the novels themselves, which don't so much as hint at this (even throwing in a convenient red herring or two) until the Reveal near the end of the last one.
The Black Witch Chronicles: It turns out that the character everyone assumes to be the Icaral of Prophecy, who is according to said prophecies fated to fight the heroine (the second Black Witch) in a battle that will determine the fate of the world... isn't. The real Icaral of Prophecy is a completely different character. His secret identity can be discussed pre-reveal without many spoilers, but afterwards is a different matter.
Accelerator is the main antagonist of the third volume. In the fifth, he undergoes a HeelFace Turn, receives brain damage that severely limits his power, and becomes one of the series' protagonists.
Othinus. Being a major antagonist who actually wins and destroys the world would be a major spoiler on its own. But after that, she undergoes a HeelFace Turn and loses almost all of her power, and ends up moving in with Touma as a second freeloader.
Coronzon is a demon who possesses Lola Stuart for the entire series and is the one responsible for all of her actions. Any discussion of it will also spoil the fact that Lola is actually Lola Zaza Crowley, the daughter of Aleister Crowley.
Codex Alera: Araris Valerian is supposed to be dead. Fade, the slave working for Bernard and Isana, is supposed to be brain-damaged. So when he pulls a Big Damn Heroes at the end of the first book and gets his real identity revealed to a few people in the process, it's a shock. He does keep the act up for a couple more books, but once he stops pretending the cat is officially out of the bag and it gets hard not to spoil everything.
Tav is one as well. His identity as Septimus' son isn't revealed until book three, although a number of facts that he's actually Gaius Octavian are fairly obvious (including his name) and the fact is fairly heavily implied even before characters are openly discussing it. The fact that Arais Valerian stayed behind in the middle of nowhere and spends his time watching over a random young shepard boy is enough to clue in several characters who learn about Arais' identity.
Jynn Ur'Gored in The Dark Profit Saga. The big reveal about him in book 1 is that he's the son of the Evil Sorcerer/liche Detarr Ur'Mayan. In book 2, he's forced to reveal that he's not a noctomancer (lunar mage) but an omnimancer (can use both lunar and solar magic), even though he hasn't used solamancy (solar magic) since he was little, as omnimancers are treated like lepers in this world. Both times this causes his burgeoning relationship with solamancer Laruna Trullon to hit a major setback.
Wendel Maculatum, from The Oaken Throne, is introduced as a kindly, if dim-witted, jester who becomes a traveling companion of the main characters. However, it turns out later that he is the diabolical High Priest of Hobb, which changes the way the character is perceived so much that most any details about him would have to include spoilers.
In Thomas, an idiotic but seemingly well-meaning mouse named Dimlon befriends Woodget and Thomas. Little do they know, he is really Dahrem Ruhar, a murderous and sadistic adept of the Scale who has gained their trust merely to steal the ninth fragment of an egg in which the serpent god Sarpedon will be reborn. When discussing Dimlon and his part in the story, his true identity would almost have to be mentioned at some point.
Raguel and Uriel in The Dinosaur Lords, due to them being named only in the epilogue and carrying a massive Wham Episode on their shoulders - not to mention that as Grey Angels, they set up a massiveSequel Hook.
You want to avoid spoiling the fact that Thomas is Harry's half-brother? This is going to significantly limit your ability to explain either of their motivations for most of their interactions after Blood Rites, starting with "Why does Harry immediately go to a vampire for help?"
Molly Carpenter, Michael's oldest daughter, who has magical talent and becomes Harry's apprentice. And then even that information became obsolete.
Margaret Angelica "Maggie" Dresden's very existence, as the daughter of Harry and Susan Rodriguez, is a massive spoiler, as the reveal that she exists at all kicks off the Wham Episode known as Changes.
In Ender's Game, the very fact that Mazer Rackham appears in the story at all is a rather massive spoiler, since he's introduced in an early chapter as a legendary war hero from the first Formic War — who should be long dead, as the war takes place over a century before the main story. It's not until the third act of the book that we find out that he's still alive, as the International Fleet used the relativistic nature of space travel to ensure that he would be alive to advise the commander of the human counterattack.
In The Gone-Away World, the hero doesn't actually exist until about halfway through the book—before that, he's a figment of his best friend's imagination.
The plot of Gone Girl sounds a bit boringly familiar without knowing the reveal that Amy Dunne has set the whole thing up.
Pretty much any non-inconsequential character introduced in or that plays a significant role in The Forerunner Saga of Halo, since it takes place one hundred thousand years prior to the primary time period of the franchise, and sets the stage for every other current piece of media for it.
Harry Potter: Sirius Black and Peter Pettigrew. There is no way to give an accurate description, however brief, of either character without spoiling The Reveal at the end of Harry Potter and the Prisoner of Azkaban. In subsequent books, both appear on a recurring basis with their true natures taken for granted.
Heretical Edge has plenty, though some have moved out of that status as the story progresses. Tabbris is the most extreme - literally any information beyond the existence of a character by that name spoils the biggest twist so far, and even that can spoil an attentive reader.
Alma Coin from The Hunger Games series is the president of District 13. Up until the end of the second book it's believed that District 13 was wiped out 75 years prior. It's not even hinted that it still exists until fairly early in the second book.
Lunar Chronicles: Ze'ev Kesley, aka Wolf. It is hard to say very much about him without spoiling the fact that he is a Lunar soldier who is still actively working for them (albeit increasingly conflicted) through most of Scarlet. The character page has separate sections for Wolf and Ze'ev, the latter of which is almost all spoilers.
Mistborn: The Original Trilogy: Saying anything about Marsh after about the early sections of the first book is a massive spoiler. Talking about Kelsier is a pretty big spoiler in the same book, of course. You can't really mention Ruin without massively spoiling the twist ending of the second book, and discussing TenSoon and OreSeur during the hunt for the enemy Kaandra in Hero of Ages becomes a spoiler very fast.
There's also Mistborn: Secret History, a book that the author has said the mere knowledge of its existence is a spoiler of sorts for the original series. The first few pages spoiler a major part of the first book, and the rest of the book literally spoils the entire trilogy for anyone who hasn't read it.
The Mortal Instruments: Anything about Sebastian/Jonathan Morgenstern from the later part of City of Glass spoils several plot points like: Jace and Clary aren't really siblings, the real Sebastian Verlac has been Dead All Along, and Valentine fed Jocelyn demon blood while she was pregnant.
Meta-level: In The Nine Wrong Answers by John Dickson Carr, there's a character in a scene who is not who he's thought to be. Once this is revealed later on, the narrator explicitly points out that he didn't use the character's name at any point in that scene.
Noah from The Raven Cycle is a bit hard to talk about without giving away the end of the first book. There's not really much to say about him that wouldn't spoil anything outside of "He's the quiet one." Heck, you can't even use his last name without giving something away.
In the Rivers of London series, PC Lesley May is introduced as The World's Most Beautiful Woman and the series' muggle voice of restraint. At the end of book one she has her face ripped off by the villain (who'd pulled a Grand Theft Me on her) in a way magic can't fix, and spends the rest of the series teaching herself magic, then pulling a FaceHeel Turn to join the bad guys who've promised her a new face. As you can imagine, everything she does after the midway point of book one has to be spoilered out. This also leads to every book blurb and review containing a Late-Arrival Spoiler on her status.
Septimus Heap: It's impossible to talk about Septimus without revealing he did not die at birth. Heck, the series as a whole is even called Septimus Heap. It's pretty obvious once you get maybe halfway through the first book that this "Boy 412" character isn't who he thinks he is.
A Song of Ice and Fire is such an extreme example of this, it is nigh-impossible to give an overview of the series without giving one and a half spoilers. Especially in the later books. For example:
The fact that Daenerys' Not Quite Dead nephew Aegon even exists is a massive spoiler even without getting into his actions.
The Three Eyed Crow who has been reaching out to Bran used to be Brynden Rivers, otherwise known as Bloodraven.
And now, there is Leaf, the first Child of the Forest to make his appearance.
The White Queen, initially presented as the Top God of the setting, is actually an Eldritch Abomination who is Yandere for the main protagonist Kyousuke. It's impossible to discuss the series without spoiling this, given that she's the main driving force behind the plot and Kyousuke'spersonality.
The Colorless Little Girl Dedicated to a Single Goal, whose mere name is a major spoiler. All Unexplored-Class are female entities with a color in their name, so just being called "Colorless" singles her out as being different from the rest. The latter part of her name hints at the fact that she was made specifically to defeat the White Queen.
Natalie Dashkov's villainous nature is a shocking surprise in the first book. All later mentions of the deceased character spoils the surprise for readers who haven't read the first novel.
You can't really talk about the second half of Warbreaker without revealing that God King Susebron is a perfectly harmless figurehead rather than an Evil Overlord and Bluefingers and Denth are not allies of the protagonists but the Big Bad and his Dragon with an Agenda respectively.
Whyborne And Griffin: It's pretty much impossible to mention Persephone at all without massive spoilers for the first half of the series. The audience isn't even made aware of her species for several books, much less anything about her personally, but she becomes integral to the plot and a part of the core characters.
Jayfeather, Lionblaze, and Hollyleaf: it's hard to mention them in examples without mentioning the fact that they're actually the result of Leafpool and Crowfeather's forbidden relationship, not Brambleclaw and Squirrelflight's kits. Hollyleaf also later attempts to kill Ashfur and vanishes from the Clan for several books, believed to be dead.
Ashfur is a minor character, right up until his attempted murder of the protagonists (which forms the climax of Long Shadows). Because what characterization he got was so bound up in that one action, it's really hard to say anything about his morality or character arc without spoiling it.
Most examples relating to Rock have to do with his being an immortal watcher who knows all of the prophecies that ever existed.
Any mention of SkyClan, the lost "fifth Clan" that was once disbanded and reformed, whose very existence is a massive spoiler for Firestar's Quest and the sixth series.
Pretty much everything about Scion is a massive spoiler in Worm. It's at least possible to discuss Scion's actions prior to his rampage without spoiling things. Eden, Abbadon/The Third Entity, Khonsu, Tohu and Bohu can't even be referred to by name or description without giving away the biggest twists.