Kevin Spencer had scenes like this every episode. They're usually something small (like Allan passing wind so hard he takes off like a rocket) or take up a whole scene (such as when Anastasia molests a bunch of trees, throws up, passes out, then is accosted by wildlife.) This makes sense, considering Kevin himself regularly loses his train of thought, and deviates from his plans rather quickly.
The entire time/dimension travel sequence in Transformers Armada, that happened without explanation (despite the gobs of mystical advanced technology lying around), is never mentioned again, and really does little to advance the plot. The only thing we learn is that the Mini-Cons rejected Unicron and gained sentience because the kids went back in time and showed them how much they cared about their beepy robot friends. And since it's never mentioned again, it's ultimately a pointless plot twist.
Some episodes of Chowder feature at least one instance of a pink fuzzy gorilla-looking thing named Kiwi appearing without mention to deliver a one-liner or a piece of exposition, then disappearing. He was only acknowledged once or twice.
I guess this is just Lampshade Hanging, but in the episode where they were digging under Mung's rival's house to steal a hoard of gems, they encountered... a big alligator.
There's also the time when Chowder was trying to get Mung to try his nauseating new dish, "foofinscoops". Mung balks at the prospect. The camera then cuts back to Chowder, who is suddenly in drag, with a blonde wig and makeup, and he says "Pretty please?" in a sultry voice. Mung shouts "WHAT THE-?!?" One second later Chowder is back to his normal appearance and voice and it's never mentioned again.
Family Guy might as well be called "Big Lipped Alligator Moment: The Animated Series," with all the nonsensical moments that have no bearing to the plot it has (and that's not including the constant cutaway jokes that always start with "Remember the time I..." or "This is just like that time I..." or "This is worse/better than when..."). Here's a tip: you know the writers have gone too far when even South Park (whose humor was all about the Big-Lipped Alligator Moments and Toilet Humor until at least seasons seven and eight, when it became The Simpsons with a TV-MA rating, in terms of humor and satire) is calling you out for having bizarre moments that have no bearing in the plot — by creating a two-parter episode about it (season ten's "Cartoon Wars").
Invader Zim has one of these in "The Girl Who Cried Gnome". Zim unleashes a robotic gopher on a Girly Ranger who's trying to sell Ninja Star cookies to him. After trapping her leg in a tunnel dug by the robot, it begins dancing and is spontaneously sucked into another dimension.
"Huh... I don't remember programming that..."
Played for laughs in the Halloween episode. Right before the mook reports back to Halloween Bitters that Dib didn't care about Zim possibly dying we're treated to a pan-over of the skool. There is a swarm of bats flying out of it, however just a second later there're dancing skeletons in tophats.
Before the dream, Tigger mentions the Heffalumps and Woozles and says they like to steal honey, then he leaves Pooh's house and the dream kicks in after a few minutes or so.
However, this still qualifies as a BLAM since Pooh never refers to it again after it's over.
While played straight for the film alone, it's inverted for the Winnie the Pooh series as a whole, where later features would show Heffalumps and Woozles as Real After All.
On the episode "Humiliation 101" of My Life as a Teenage Robot, once Jenny figures out that she in fact will not be embarrassed by her mother in front of the entire school, she breaks into random song with Brad and then they proceed to school after singing this little ditty with a small dance included as if nothing ever happened.
Hanna-Barbera's feature Heidi's Song had not one, but two. First, Grandfather tells Heidi stories about evil spirits haunting the mountains right before she goes to sleep, leading to a Disney Acid Sequence nightmare; second, when Heidi is locked in the rat-infested basement by Fräulein Rottenmeier, the rats break into a Villain Song, with Sammy Davis Jr. as the head rat. (And for this BLAM, Davis gets second billing on the movie, right after Lorne Greene as Grandfather and before Margery Gray as Heidi.)
In the Chucklewood Critters TV special "Which Witch is Which", Ranger Jones leaves his Halloween party to investigate something, but when he does, the scene cuts to a pointless music video showing these witches that perform all these magic spells. This segment/song holds nothing to the plot at all.
Dexter's Laboratory had an episode where Dexter is stalked by a little girl with enormous, soul-penetrating eyes. While the episode, like most episodes of the series, contains little-to-no background music to maintain a quiet and suspenseful vibe, all of the sudden we're inexplicably treated to a colorful, poppy, saccharinely upbeat musical number to illustrate Dexter's frustration. Although completely out of left field, it remains one of the more popular scenes in the show's history, and could be seen as either an Ear Worm or the show's Crowning Musicof Awesome.
A straighter example appears at the beginning of the episode "Continuum of Cartoon Fools", in which Dexter is seen sitting at a desk, scribbling something on a piece of paper and looking at a stopwatch while periodically making a bizarre noise that sounds like "BAAAAWT". It's never brought up again, and we never do find out just what the hell he was doing it for.
He was timing a storyboard of the very cartoon he was in. That...still doesn't make sense, though.
In that same episode, at the end of a sequence where Dexter blocks off every possible entrance to his lab to keep Dee Dee out only to have her pop up again, his frustration reaches a breaking point, and he decides to... smash a watermelon with a mallet.
Animaniacs did this quite often, typically with quick, random cameos by other various Animaniac characters in each other's segments. For instance, it happens twice in the Slappy Squirrel cartoon "Bumbie's Mom", and Slappy lampshades it both times.
It was pretty common to see Ralph the security guard chasing Yakko, Wakko and Dot through one random scene in at least one cartoon per episode that the Warner Brothers (and Sister) weren't supposed to be appearing in. It was quite literally a Running Gag, and would usually culminate at the very end of the episode with the siblings scampering back into the water tower and Ralph shaking his fist at them.
This trope's appearance in animated films was spoofed in the Pochahantas parody they did, via "The Ice Cream Song".
In Phineas and Ferb, the popularity of the "Gitchie-Gitchie-Goo" song in one episode led the higher ups to decide to make the musical segways Once an Episode. That includes when it really doesn't make any sense to have a musical number whatsoever. The writers do their best of course, but sometimes there's just no way to work a song into the plot of an episode. And yet there's one there anyway.
"Robot Rodeo" ends with a particularly weird one "Izzy's Got the Frizzies", with an extended sequence of Isabella go-go dancing to a song about her frizzy hair. Made even odder by the fact there was a much more sensible musical number earlier in the episode.
There is no Candy in Me from "Picture This!", a spur-of-the-moment rap at the very end of the episode brought about by Candace's stunned stutter.
Buford: Nerd ain't no piņata!
"Dance, Baby" from "Candace Disconnected", where Dr. Doofenshmirtz randomly invites Perry to join in his "evil exercise show", and they start doing aerobics to a goofy disco song with nonsencial lyrics.
Dance, baby, dance, baby Hands in the air Go down to the store And buy a wicker chair!
"Shot in the Butt with a Dart" from "Bad Hair Day" has Doofenshmirtz, after getting mistaken for a rare "tangerine orangutan" and being shot with a tranquilizer dart, singing a random show-tune about it, only to lose consciousness in the middle of his song.
I'm blurry and drowsy, but balladry beckons Though I'll probably lose consciousness in seventeen seconds
For a non-song example, there is the Giant Floating Baby Head. It first shows up in "One Good Scare Oughta Do It!", where the boys try to cure Isabella's hiccups by building a haunted house. At the end of the episode, they admit that they don't even know what it was, where it came from, or why. Every few episodes it can be seen randomly appearing, though no one will ever mention it.
The end of The Simpsons episode "Burns, Baby Burns". Homer and Larry have just been caught staging a kidnapping, when suddenly the whole scene turns into a party. Lampshaded when Marge asks where the music and liquor is coming from, and Homer replies, "It's a party, Marge. It doesn't have to make sense."
Although this can be seen as a jab at how many of Rodney Dangerfield's (who was voicing Larry Burns) movies seem to end with a spontaneous party.
Specifically, it's referencing his spontaneous party in Caddyshack, which even had the same Journey song "Any Way You Want It." It was something of a BLAM in that movie, too.
The surfing ending of "The Great Money Caper" Lisa did say that the ending would be "insulting to your [the viewers'] intelligence." It's like the writers were aware that the show was getting too wacky for its own good.
In the episode "Ned-liest Catch" Homer is chasing Ned Flanders to convince him not to break up with Edna. At one point he starts swimming in a canal trying to keep up with him but he gives up and drifts away, moments later he is randomly attacked by a giant octopus.
The episode "Monty Can't Buy Me Love" has a minor one. The family is taking a stroll through the neighborhood when they catch sight of some kind of big public event happening just down the street. Marge wants to continue on her walk, but the others run off to check out the event, so Marge reluctantly tags along. The event in question is the grand opening of a new shopping mall, which isn't a BLAM per se as the mall is owned by young, charismatic Australian billionaire who makes Monty Burns envious, thus setting the main plot in motion. But as the family is waiting to be let into the mall along with the rest of the crowd, Marge notices Homer mysteriously sipping champagne from an elegant glass. "Homer, where'd you get that champagne?" she asks. Homer simply points to his right and says "Clown" - at which point a stereotypical Non-Ironic Clown named Noodles appears beside Homer literally from out of nowhere holding a champagne bottle, and refills Homer's glass. ("Thanks, Noodles.") Although an earlier shot of the event had made clear that there were indeed circus clowns on hand to entertain the crowd, the last time we see Homer before that one sequence (and that had been only seconds before) the only person standing beside him had been Bart. One commentator on the episode sarcastically wondered if Bart had suddenly disappeared, only to be replaced by a clown.
In "The Day the Violence Died", Chester Lampwick sues Roger Myers Jr. for stealing the character of Itchy from him. In one scene, Bart and Lisa are watching Krusty's show, where he introduces the replacement for Itchy & Scratchy - a Schoolhouse Rock -esque cartoon called "Amendment to Be". Granted, it's absolutely hysterical, and is related to the plot, but the length and sheer randomness of it makes it feel like a BLAM.
The gag from "Simpson Tide" where it turns out that the Soviet Union never broke up after all.
One of the Henry and June wraparounds in an episode of KaBlam!! had June going to sing a pretty song, and saying how she wanted to make the show "intimate". She also said that without Henry on the show (this is the episode where he quits temporarily), she wanted to "spread her wings", but what did that do with the plot? The song was nice, the scene was funny, but what did it have to do with the episode? The scene never got mentioned again, but only one small remain- after the following short and the commercials, June was wearing a neckbrace (she crashed into the fourth wall), but it suddenly disappeared by the final wraparound. Plus, it was very out of character for her.
Cartman's head exploding in the episode "Medicinal Fried Chicken". It didn't happen in a Dream Sequence or an Imagine Spot, his head really did blow up. But he's not Killed Off for Realout of the blue — the next time he's seen, he is relatively fine, and the head explosion is never mentioned throughout the rest of the episode. What makes this especially strange is this happened in season thirteen, after the surreal elements of the show had mostly died off.
In the episode "Eek! A Penis!", during Mrs. Garrison's chase to find his "penis" (a white experimental mouse with a human penis surgically grafted onto it), the "penis" stops fleeing at one point after glimpsing at the moon, and begins to have a duet with itself (the mouse and the penis, which can talk now) in the vein of "Somewhere Out There" from An American Tail. They are stopped midsong by Mrs. Garrison, and the "penis" never sings, or talks, again.
Then there was that one time that the plot was already resolved, and then out of nowhere, a giant bird busts through the school roof and eats Kenny.
That one is a Brick Joke related to what the agnostic couple says earlier in the episode. They said that, for all it matters, God could be a Giant Reptilian Bird in charge of everything... and the creature is exactly that. Doubly ironic in that, in the South Park universe, God exists and has a completely different (but still weird) appearance.
Clyde's angry defense of Cartman, in a voice and tone completely alien to him, at the beginning of "Marjorine":
"You sir have mocked Cartman before yet you too sit here demanding answers? Now damn you let him speak!"
in the the first episode 'Cartman Gets an Anal Probe' Cartman yells that he did not have a probe then all of a sudden the vistors zap him and he starts singing 'I love to singa!' before being zapped back to normal, the boys are speechless.
After the credits, cows are seen using a device given to them by the aliens on Officer Barbrady, who starts singing the same thing Cartman did.
Earthworm Jim has an amusing intermission in the middle which in pretty much every case had nothing whatsoever to do with the plot. The blammiest (in "Opposites Attack!") is probably "six seconds of dancing turtles".
Courage the Cowardly Dog had Eustace being attacked by a squirrel that came out of nowhere in the episode "Family Business".
One episode had the family's house being placed in the middle of a biodome. At one point, the biodome produces a thunderstorm, and when Eustace grabs the front door handle to look outside, the handle gets zapped — and in the middle of Eustace's electrocution, a duck's head gets overladed across his butt and quacks.
One episode opens with an archeologist dusting off a gem stone inside some sort of temple, which suddenly shoots out a beam of light, which is reflected off a few things before causing a disco ball to come out of the ceiling and some music to play for a brief moment. Afterwards, the archeologist just shrugs and continues where he left off.
An early Bugs Bunny cartoon, Fresh Hare, ends with one of these: Bugs has been caught by the RCMP, tried for many serious crimes, and sentenced to death. An early Elmer Fudd (the fat one) asks him for his last wishes, and he replies "I wish... " and the entire scene becomes a blackface minstrel number of "I Wish Was in Dixie." This scene frequently gets censored out of the cartoon.
The Porky Pig cartoon Porky at the Crocadero has a scene where the walrus manager goes off to get Porky to provide music for the restaurant, saying "I must get him back schnell!". As he starts to run, the picture suddenly freezes and an offscreen voice shouts "Ladies and gentlemen, 'schnell' means 'quick'!". The picture then starts again like nothing happened.
Another Porky cartoon, Porky's Duck Hunt, a duck lands on a cask of booze, but just as Porky shoots at it, the duck flies away and he shoots the cask instead. Five fish swim into the sunken cask, then stumble out drunk, walk on land and get in a rowboat and start singing "Moonlight Bay". Even Porky seems confused by the events.
The Jimmy Two-Shoes episode "Ghostsmackers" goes into a commercial for a ghost-related Misery Inc. product. It gives nothing to the plot, and the product is never scene again.
It's pretty clear that this fight is a hallucination even before it begins, but even amidst all the other weirdness, Guru Pathik's brief cameo during the fight comes out of nowhere and, unlike the fight, is never even discussed.
In Home Movies, in Brendon's production of "Starboy and the Captain of Outer Space", the conversation turns to hot dogs and how they're made - there's an abrupt cut to a still-picture montage of the two visiting a hot dog factory with a guy in a hot dog costume, with a bossa-nova soundtrack, and right back to the action...in the space of maybe three seconds. One might wonder if one even really saw it.
The American Dad! episode "The One That Got Away" has Klaus throw a smoke bomb on the floor and vanish from sight. A moment or two later, there's another blast of smoke, and when it clears we see Klaus, now with a sword and crown, cutting his way out of the belly of a Lovecraftian monster. This event gets precisely three lines of discussion before being forgotten about entirely:
Klaus: I don't know, but wherever it was, I am their king now.
The "Crack" medicine commercial parody on "A Jones for a Smith". Yeah, it works as a satire on how prescription meds can be just as bad as illegal drugs, but, like most gags in Seth MacFarlane's cartoons, it doesn't really have a relevant place in the plot. Of course, unlike a lot of gags in Seth MacFarlane's cartoons, the BLAM is justified as Stan was hallucinating from the crack and saw his life as a prescription drug commercial (which ends with him cuddling up to the homeless crack dealer's mother [whom Stan saw as a dog during his hallucination] on a dirty mattress in an alley).
The Smiths singing "We Go Together" in "Home Wrecker".
The BBC Christmas animation The First Snow of Winter is the story of an Irish duckling who gets seperated from his family while flying south, and is befriended by a water vole. About ten minutes in, for no real reason, Voley and Sean start line-dancing. And then an entire flock of sheep joins in. At the end of the scene they spin around to look at the sheep grazing as if even they're wondering whether that really just happened.
The Sea Pony scene in My Little Pony: Rescue at Midnight Castle. Everything's been semi-serious up to that point, and then Megan and a Pony fall in the river and get eaten by a giant clam. CueDisney Acid Sequence in which the Sea Ponies rescue them while singing a catchy doo-wop song (and judging by their expressions, Megan and Applejack are just as confused as the audience). The whole song is never mentioned again, although the Sea Ponies themselves later help Megan and the Ponies sneak into Midnight Castle.
Friendship Is Magic: Most of Pinkie Pie's song sequences are BLAMs (or come pretty darned close), but her over-the-top flash dance routine at the beginning of A Friend In Deed really takes the cake. It's especially noteworthy since it's one of the few times you see a character from the showwear pants.
Likewise, Discord's "Glass of Water" song from "Three's a Crowd".
"Fools in April" has a scene where SpongeBob is laughing so much from pulling pranks that his tongue appears to fall out...which in and of itself is another prank, as not only is it a fake tongue, it's alive, laughing alongside SpongeBob. This odd entity appears for a few seconds and is never explained or mentioned again.
Finn's Premonition Dream in episode "The Lich" symbolically foretells of the reappearance of the Lich. Being the type of dream that it is, it features the Cosmic Owl. In contrast to Jake's "croak dream" in "The New Frontier" where it appeared at the end of said dream, as if it were a psychopomp, in Finn's case it's seen on the screen of the iMac lookalike computer he's cracking up in front of.
In the Metalocalypse episode "Fatherklok", Toki, Murderface, and Pickles all express their disdain for their respective fathers... when seemingly out of the blue, Nathan disagrees with them, and the show cuts to a montage of Nathan and his father doing fun, stereotypical father-son activities together, accompanied with cheesy, overly happy music.
Also when Toki sings Underwater Friends, presumably they're still recording and listening to that craziness, but not Toni's Hamburger Time Disney Acid Sequence because clearly that was a dream.
An episode of Justice League Unlimited titled "Kid's Stuff" had a rather funny one. It features a baby Etrigan randomly appearing. We never find out how or why he got there.
Bender: When I grow up, I wanna be a steam shovel!
Another moment involving Bender has a scene cutting to him, on fire, screaming and flailing about, whilst sitting in a chair. Several of the crew then run on-screen and put him out with fire extinguishers, and then Bender procceds to calmly resume smoking a cigar.
In the short-lived Clerks: The Animated Series, during the episode where Dante Hicks is being sued, they suddenly declare that the original ending got lost on its way overseas and the Korean animators were forced to animate another ending, which ends up being a bizarre anime.
The early Betty Boop cartoons were racy, surreal, and featured a lot of hot jazz music and vocals by the original king of cool, Cab Calloway. These musical numbers were often BLAMs, though, as in "Minnie the Moocher", in which Betty is very suddenly and for no apparent reason accosted by a singing, dancing ghost walrus (a rotoscoped Calloway). Yes, a ghost walrus, who then proceeds to sing the eponymous song for no reason at all. This is pretty strange even by the standards of early Betty Boop.
In the episode of King of the Hill involving Peggy, Nancy, and Minh in a race for school board, there's a scene where Dale goes to a trailer park to pick up voters who are likely to be Nancy supporters. No-one is at the trailer-park except a man fixing a satellite dish (the others having been abducted by Peggy to stop them from voting for Nancy). The man explains that the people are gone, and then decides to assault Dale for Dale's hat, quickly scaring Dale out of the park, the last part specifically being the BLAM moment.
In 'Peggy's Pagaent Fever", after Peggy's makeover, the scene switches to Bill washing his car while singing (badly) to BTO's Takin' Care of Business, when Peggy passes by in Buck Strickland's car while Bill just stares.
Yashimoto trying to fight a Fixed Idea in Cyber Six. He starts throwing out some goofy martial arts moves and yells, which is completely in character for him. Then right the hell out of nowhere Jose, the goofy little kid who can't fight to save his life, muscles in and starts throwing moves and yells of his own. He ultimately tries a jump-kick and falls flat on his back, and one of the Fixed Ideas has enough and and attacks Yashimoto. Watch it here at the 7:35 mark.
Trina Riffin's Diary Moments are apparently an in-universe example of these to anyone not into Grojband, even Mina lampshades this in "Knight to Remember" after having one due to having her personality swapped with Trina's.