"The children are suddenly surrounded by a couple of wildcats who prepare to slaughter the children until a man shows up on another bus with a rifle and shoots it at the wildcats. If none of this makes any sense, that's okay, since it's never refered to ever again."
Passepartout, in his joy on reaching at last the American continent, thought he would manifest it by executing a perilous vault in fine style; but, tumbling upon some worm-eaten planks, he fell through them. Put out of countenance by the manner in which he thus "set foot" upon the New World, he uttered a loud cry, which so frightened the innumerable cormorants and pelicans that are always perched upon these movable quays, that they flew noisily away.
There's that uncomfortable and unnerving "Vodka" chapter that comes the eff out of nowhere late in His Dark Materials. Will, a 12 or 13 year old boy, is traveling alone. He stops at the house of an old priest to ask for directions. The priest pushes him into accepting a drink of vodka, chats in an overly friendly manner, is very touchy-feely, tries to convince Will to stay a while and is just generally creepy. After few pages of this, Will insists on leaving and the man gives him a hug and lets him go. There is no mention of the incident or the old man ever again.
In addition to a number of Wacky Wayside Tribe incidents, one can probably find a number of Big Lipped Alligator Moments in L. Frank Baum's Oz books. The first book, The Wonderful Wizard of Oz, has the China Country, where all the inhabitants are made out of china. Some of them, such as the singing china clown, have been broken and mended several times. They neither help nor hinder Dorothy and her friends, they are introduced out of nowhere and have nothing to do with the story, and they're never mentioned again in the book afterward (or in any of the later Oz books, for that matter). Things like this add to the unnerving dream-logic of the story. Word of God all but admits that the China Country only exists to pad out the length of the journey from Point A to Point B.
There is a particularly narmful scene in Of Mice and Men where Lennie hallucinates that he is being berated by a talking rabbit. And his Aunt Clara.
The Lost Symbol has a chapter where the hero is unconcious... literally. Not mentioned again, not used, nothing, whole chapter = sleeping hero.
The episode of the dinner of Trimalchio in Petronius' Satyricon. It also happens to be the only passage that survives intact.
Earlier in the work, there's a scene where the main characters get drunk, are (forcibly) involved in an orgy, pass out, and wake up with their faces covered in soot. They vow never to speak of the incident again. Several other scenes might also qualify - the fragmentary nature of the work makes it hard to tell what is and isn't relevant to the plot. Or even what the plot is.
Mervyn Peake's Gormenghast series has many random scenes, where characters are introduced and conduct pointless dialogues, or new locations are visited and lovingly described, and are then never mentioned again.
Considering that he only finished two of the five planned books and only one additional one was made (by his wife), this might be a case of foreshadowing destroyed by Author Existence Failure.
A bizarre example from a factual book can be seen in Black Like Me, the journal of a white man who changes his skin colour and observes the way he is treated as a Negro man, as he calls it. On a bus to Mississippi he encounters a black man named Christophe who sings Jazz, smiles at the white folk and snarls at the black folk, speaks perfect Latin, was training to become a priest, claims to be meeting his wife in another town and is planning on shooting several men and running away with his family. Straight out of nowhere, inexplicable, never mentioned again.
In the first or second chapter of Moby Dick, Ishmael (the protagonist) is in a tavern, where there is a man named Bulkington, from Virginia. The way he's described makes him seem both magnetic and physically impulsive, and others in the bar are shouting his name. Then he's never mentioned again. (Even my English teacher thought that was strange.)
A commonly accepted theory is that Bulkington was intended to be a central character in a mutiny plot Melville originally planned but later dropped.
Oh course, this happens in Thomas Pynchon novels all the time, in fact, BLAM's may get more page space than the novel's "plot" itself, leading one to wonder whether it is, in fact, the plot of any Pynchon novel that is a BLAM to be compared against the self-consistent cohesion of the otherwise unrelated, ubiquitous absurdities.
As it goes on, Stephen King's Dark Tower series starts to have more and more of these. One that springs to mind is in the scene where Roland and Eddie meet Stephen King, who is a character in his own book. Now, that may sound Blammy but it all makes sense in the series' metafictional context. The BLAM here comes when Eddie comments that if King-the-character keeps smoking, he won't live long enough to complete their story. Roland then insists that smoking is good for you as long as you wait until you're an adult to start. Apparently it keeps away everything from insects to evil spirits that cause disease. It seems like it could maybe be a Chekhov's Gun, but it's never mentioned again. Maybe it was just a way of placating Moral Guardians incensed that Roland was smoking?
Fans of the Dark Tower series were worried that King would die before he completed the series because he kept taking too long between books and he was a heavy smoker. Eddie is serving as a stand in voice for the fans who want their story to be completed and Roland is a stand in voice for King, who politely but firmly rebukes Eddie.
Hmm. That makes some sense, but the scene on the whole comes so out-of-the-blue and is never mentioned again and has so many bizarre touches (does King really believe that smoking is good for him? Is what Roland says true in the Dark Tower universe?) that it's a BLAM. Just having Roland say something about whatever Ka wills would have been more in tune with the feel of the series and would distract far less from the story.
There are a LOT stranger scenes than that. Mrs. Tassenbaum starts out as a Big-Lipped Alligator, coming out of nowhere with a long backstory. Then she finally meets Roland, and it becomes a Big Lipped Alligator Episode when they eat fried chicken and have sex in a hotel room. She doesn't really help Roland, and I guess I can infer that her only purpose in the story was to get him to a hotel room where he could see a television and not be able to see anything but scan lines. There are more scenes like that, especially in the last three books.
Didn't help Roland? Who drove him to the two important places he needed to be? I doubt the ancient Roland knows how to drive a stick.
In the children's classic The Wind in the Willows, there's the infamous 'Piper at the Gates of Dawn' chapter, where the characters are transported into a mystical world where they meet the great god Pan. Many editions of the book omit this chapter, not because it's bad, just because it's so baffling in relation to the rest of the story. 
Two chapters earlier, there's a whole side-story where the main characters are nearly lured to a life at sea by a siren. Like the Piper at the Gates of Dawn, this too comes out of nowhere and is never heard of again.
While it still probably qualifies as a BLAM, the lurer is a wizened old ship-going sea rat who beguiles Water Rat. It's a pretty clear shout-out to The Rime of the Ancient Mariner.
Older Than Feudalism: At the end of book 19 of Homer's The Iliad, as Achilles hitches up his horses to go into battle, he prays that they will bring him back safely like they didn't do for his fallen friend. In response, the horse Roan Beauty suddenly gains the power of speech, simply to tell him "yeah, alright, this time. But next battle, you're doomed, buddy." Aside from a moment of surprise, Achilles barely seems to notice his brand-new talking horse; Roan Beauty loses speech as suddenly as he gained it, and the incident is never, ever mentioned again.
In World Made By Hand there is a scene where Robert visits the New Faith congregation. While there, he meets an obese woman that has multiple seizures followed by prophecies. The general reaction readers appear to have to this scene is "what the hell?"
Deke McClelland's Photoshop 4.0 Bible (as the title implies, it's a how-to guide) pulls one off at the very end, after several hundred pages of Rapid-Fire Comedy: in the middle of a step-by-step guide to making a graphical effect, step 29 is a snippet of a suspense story about a spy sneaking through the dark. And halfway through, the Prime Minister pops up out of nowhere only to get shot. (So, a BLAM - both a figurative and a literal one, to boot - within a BLAM!) The author then goes back to Photoshop tips, commenting that he dislikes Step 29, since it's troublesome and makes all others look dull in comparison.
DOS For Dummies included, among its many how-tos on MS-DOS, step-by-step instructions on how to change a nappy.
Arguably the entire two or three chapters featuring the hobbits' adventures with Tom Bombadil in The Lord of the Rings is a very lengthy BLAM chiefly about singing excruciatingly bad folk songs and talking about how awesome Goldberry is. Actual connections to the plot of the rest of the book amount to: (a) the One Ring doesn't work on Bombadil - which gets one mention at the Council of Elrond -- and (b) leaving the Old Forest you might trip over a wight and wind up with a cool Numenoréan sword.
In the middle of the original Gaston Leroux novel The Phantom of the Opera (well, at least in the original English translation,) a man on fire runs through an underground passage at one point, scaring the protagonists and then just as quickly runs right out of the scene and the novel and no one ever talks or thinks about it afterwards.
There are actually several bizarre encounters in the cellars of the opera house. They are all BLAM's to some extent, but their main purpose is probably to give the feeling that the protagonists are leaving the real world and are on the Phantom's turf now. Note that Christine's description of her first journey into the cellars, features some fairly strange and hellish imagery too. Some critics have seen the journey into the opera house cellars to be evoking The Divine Comedy, and Dante's descent through the Circles of Hell, so if this is the case, at least the BLAM's have some purpose to them.
Greg lampshades this in The Last Straw with Fregley coming out of nowhere with icing on his face and saying "BOOGIE! BOOGIE! BOOGIE!"
The Philosophy Club scene in the novel version of Gregory Maguire's Wicked. It seems like it should be a metaphor for something, but no one knows what.
A lot of Louis De Bernieres' Birds Without Wings could be said to be a patchwork of BLAMs. There is one scene where you see the sack of Smyrna from the point of view of one of the minor characters as he drowns, and the chapters about Mustafa Kemal Ataturk contribute to a feeling that the whole book is merely filler with a few relevant chapters pasted in. Even the character through whose eyes we see much of the Ottoman experience in World War One is not the character who then goes on to go mad and kill his girlfriend.
After an assassination in the Vietnam War novel War Dogs, the group's leader is returning from his watching post and is suddenly attacked by a tiger. After an extended river tiger fight, he regroups with his team and almost no time is spent discussing his fresh wounds.
The two-dimensional planet stop in A Wrinkle in Time. The heroes "tesser" to a weird place where the children feel squashed and can't see anything, one of the adults mentions something about the kids being unable to exist properly on a two-dimensional planet, and they warp away. It was probably supposed to be related to the four-dimensionalness of their teleporting method, but no actual explanation is given for why they went there, what the heck a "two-dimensional planet" even is in a three-dimensional universe, why the kids weren't crushed to death, or how the adults apparently are able to survive on such a planet.
To be fair, there actually is an explanation for a couple of these: the "adults" are actually an unspecified kind of supernatural creature which doesn't even need to take a corporeal form, therefore making it perfectly reasonable that they wouldn't suffer the same ill effects as the children. In fact, the adults find it "amusing to be flat" and it's implied that the person in charge of the tessering just plain forgot that the children would be harmed by it. The other points still stand, however.