In the episode "Fa La La La Ed", while Jimmy is complaining to Sarah about the pain of smashing his piggy bank, we see Ed falling over as he tries to prop up some Christmas lights.
In "Look Before You Ed," while Edd and Jimmy are covered in snow in the foreground, Eddy and Ed steal Kevin's snowboard in the background.
Parodied in the Futurama episode "That's Lobstertainment!" Zoidberg's Uncle, Harold Zoid, tells the extras in his film to throw a bit of humor into the background of a dramatic scene...which results in said extras running around screaming and throwing pies at each other. Later its mentioned that they spent the entire budget on pies before they could complete post production.
In the episode "Mission: Responsible" of The Fairly OddParents, the first time Wanda dials Timmy, Cosmo tries to find out how a napkin (even a plate!) works!
Rocket Power was actually quite fond of this trope. Whenever there was an episode where a camera was involved (i.e., Twister shooting a documentary, or even the news), there was something funny going on. During the episode about a documentary of Otto and his Sno-Mart ventures, you can see this trope playing through a LOT. Such examples include Ray coming out and dumping garbage all over the front lawn, a skater in the Blader Bowl flying out...then an empty skateboard coming out, and another where it was repeated, except a dolphin flew out of the Blader Bowl.
There was also an incident in which a news reporter was complaining about how there wasn't anything to film, and then right behind him, a flying saucer comes in, pulls a whale out of the ocean, then flies off.
Avatar: The Last Airbender: After the whole 'Appa ate Momo' incident, when the Gaang is talking about where Aang got off to, Sokka can be seen trying to get out of Appa's mouth, then slipping on the drool, twice.
Even the people who did the small annotations comment on the event! (This is from the marathon Nicktoons aired leading up to the premiere of The Legend of Korra.)
When Prince Zuko and Iroh are invited aboard Commander Zhao's ship, Zuko and Zhao have a rather intense conversation in his cabin, while Iroh occupies himself by looking at a set of polearms leaning against the opposite wall. At one point, Iroh accidentally knocks them all over, scrambling to catch them with a huge wide-eyed face before putting them back in place. The whole thing lasts less than a second.
When Korra sneaks into the pro-bending arena, she's caught by Toza, who believes she's trying to watch for free. While the two bicker, Bolin walks by in the background, backpedals a step or two, and stops to fix his hair before conveniently interrupting the argument with awkwardness galore.
Something of a Funny Sideground Event: When Tarrlok interrupts dinner at Air Temple Island, Pema gives Tenzin a Death Glare for allowing Tarrlok to stay. Then, when Tarrlok sits down to talk to Korra, Ikki can be seen doing the exact same glare as her mother, even after the camera isn't focusing on her anymore.
Winx Club: Stella wakes up from a sleeping gas induced slumber, finds a ladybug on her arm, and runs around in the background.
In the Family Guy episode "Fifteen Minutes of Shame," in which the Griffins get their own reality show, an argument at a seafood restaurant between Meg and her parents is hard to focus on while Stewie's fighting a live lobster in the tank behind them.
"Movin' Out (Brian's Song)" has Peter and Lois conducting a kitchen-table conversation while a seeming Simpsons promo at the bottom of the screen morphs into Quagmire sexually assaulting Marge Simpson.
In "Screwed the Pooch", the trope is not only lampshaded, but dressed up and sent to walk the streets as a serious conversation between Lois and Brian becomes completely secondary to the fact that Peter has just farted in the soundproof booth he has locked himself in, and is increasingly desperate to escape his own gas before collapsing into unconsciousness.
Family Guy does indeed love this trope: "The Story on Page One" had a discussion between Meg and Lois in the kitchen, while out the window a mind controlled Chris turns on Stewie and attacks him.
Another twist on this trope comes in "Let's Go to the Hop" when Peter and Lois are getting ready for bed and calmly discussing an issue about Meg. While donning bondage gear. None of the dialogue alludes to this until the very last line.
In "Peter's Two Dads", Peter announces that his father Francis has died. Lois and Brian (who never liked Francis) express sympathy, then leave. As Peter continues talking, through a window behind him we can see Lois and Brian dancing with joy on the front lawn, Brian grabbing Lois' chest, and her slapping him.
At the end of another episode "Long John Peter", Chris tries to apologize to Anna, the young vet he has a crush on whom Peter suggests that he'd act like a jerk to, by bringing in a badly beaten Brian. While the two of them have a conversation, Brian wobbles back and forth for a few seconds and then falls over.
The episode "He's Too Sexy For His Fat" has Chris and Lois talking about liposuction. While Lois wonders aloud what kind of idiot would go through such a procedure (right before a newly-thin Peter walks through the door), an overweight Stewie who is stuck in his high chair tries to get at a chocolate cake that Lois left on the counter.
In "I Never Met the Dead Man", Peter and Chris chat while Stewie can be seen retrieving the satellite dish Peter crashed into earlier in the episode.
In "Chitty Chitty Death Bang", while Lois complains to Peter about not being able to find a place to hold Stewie's first birthday party, Stewie can be seen using large suction cups to climb down the window. As the conversation continues, he gets stuck and falls to the ground after attempting to free himself.
In "Business Guy", Lois talks to Peter while Quagmire, after ripping a chunk of his skin off, runs around and crashes into his airplane.
In "Big Man on Hippocampus", Lois and Peter reunite while Quagmire tries and fails to prepare to make love to Lois. His failed attempts continue as Peter and Lois exit his house.
"Christmas Guy" features Peter and Lois having a conversation, oblivious to Stewie stealing a house's Christmas lights, putting lipstick on a snowman before kissing and beheading it, and eventually blowing up the entire town.
In "Friends Without Benefits", when Meg and Chris have a conversation in the living room, Peter can be seen outside using his Slip n' Slide.
In "The Peanut Butter Kid", when Lois is introducing Stewie's commercial to the family and neighbors, Chris can be seen eating nuts.
In the first episode of The Avengers: Earth's Mightiest Heroes! (not counting the "season zero" pilots), as Thor is talking to Jane Foster after saving her from an uncontrolled car, we see said car's driver struggling to get out with the seatbelt jammed. When the scene finishes, the driver gets a face full of airbag.
Borderline example from The Simpsons: Homer is having a relatively mundane conversation with his recently-new boss, Hank Scorpio, about how he's thinking of quitting and moving back to Springfield for the sake of his family. While this is going on, a massive battle worthy of the climax of a James Bond movie is happening in the background, but Homer doesn't seem to notice. Scorpio himself is killing ninjas and elite secret agents with a flamethower and launching a Doomsday Device during the whole conversation — which means it isn't completely in the background, but the effect is the same. At the end of the sequence, the background event comes to the foreground as Homer kicks a grenade out of his way before leaving.
The episode "Jazzy and the Pussycats" featured Lisa adopting a load of abandoned and unwanted animals, and whilst trying to find owners, Chief Wiggum's car breaks down, so Lisa gives him an ostrich to ride away on. Later on in the background, you can see Chief Wiggum (still riding the ostrich) leading an arrested Snake away (on another ostrich).
There's another example in the episode in which Bart become a boy scout; while seeing television with Homer and Lisa, Bart criticizes Itchy & Scratchy for being unrealistic, and says that the cartoons doesn't have to be realistic. In this moment a second "Homer" is passing by the window outside.
In "The Color Yellow", the class is told to create family trees. While Lisa talks about family trees, we get a view outside of the window where Groundskeeper Willy is filling a hole in the ground with water from the hose, then sits in a folding chair and begins fishing in it.
In the Joan of Arc segment of the episode "Tales From The Public Domain", in the background of one of the battle scenes an English soldier can be seen fighting a French soldier using a teacup instead of a sword, he then gets his hand cut off and runs around bleeding profusely.
The show's opening credits also contain this trope, though you often need to freeze-frame in order to see what's going on. An early 2014 episode's credits inserted a tribute to a character played by recently deceased voice actress Marcia Wallace, for example.
In "Gal of Constant Sorrow", when Lisa tells Hettie, the homeless woman Bart took in, how talented she is, a circus performer on a unicycle can be seen coming by juggling, then goes in the opposite direction, with his head on fire, then comes back on a stretcher with paramedics on unicycles.
In American Dad! episode "Stan Time", Roger and Steve are trying to write an original, modern porno, while behind them two sexy ladies repair the air conditioning in increasingly erotic ways.
In "Stan Knows Best", when Hayley leaves to go live with Jeff, Stan tries to lure her back by yelling "rhubarb", as he had her brainwashed at age 5 to kill Walter Mondale when it's uttered. After he says it, Steve walks by in the background with a sniper rifle.
Used in Creature Comforts, both the original short, the series based on it and the various commercials made by Aardman in the same format, such as their Chevron campaign.
Ads for Hubba Bubba Max bubble gum. Not done by Aardman, but clearly influenced by them.
In an episode of King of the Hill where Dale gets a suit of armor, in the background while the other three are talking you can see him walk off a roof in his armor.
After finding out Hank is entering Ladybird in the dancing competition in "Dances With Dogs", Bobby says "You told me dog dancing was only for weirdos!" as he says this a fat man dressed as Charlie Chaplin walks by twirling a cane and walking a french bulldog.
In "Phish and Wildlife" when Hank and the ranger are discussing ways they could get rid of the hippies in the control room, on one of the monitors Bill can be seen dressed in his hippie garb stumbling around drunk, or possibly high.
Robot Chicken did this in one sketch during a song recording. The two producers at the boards turn off the sound and take five to talk all while in the background the singer finds himself assaulted by a mutant, an alien and finally devoured by a wolfman with the producers unaware.
There was also an episode where the Playmobil characters were inside the airport, talking about how silly the set was. If you watch the luggage conveyor belt in the corner, you can eventually see a Playmobil kid figure (which came with the set) rolling through.
In one sketch, a woman is sitting in a subway car, while in another car behind her a man is getting slapped and throttled by a monster.
Easy to miss example in ReBoot. While Bob is begging Phong to give Hexadecimal an icon, we can see Ray sampling Hexadecimal's biscuits made out of Herr Doctor while Mouse tries to stop him from eating one.
Used in Home Movies. An especially bizarre one comes when Brendan and his father are at a restaurant. Two men are seen at another table. One man draws an unflattering picture of the other as a severed head, and gets hit for it. The DVD Commentary said of this: "Whoa, what's going on at that table?"
During the episode "It Was Supposed To Be Funny," when Brendon is admitting that he can't finish his fries, you can see a car going through the Alien Burger drive-thru being abducted.
A Jimmy Two-Shoes short revolved around this, with Jimmy, Beezy, and Heloise complaining about how nothing ever happens in Miseryville... while the city is being destroyed in the background.
In a less than subtle example in the DCAU, Harley and Mercy fighting it out in the background while Lex Luthor and The Joker are having the business meeting during The Batman Superman Movie.
The South Park episode "A Very Crappy Christmas" features the characters watching A Charlie Brown Christmas on TV. The first two shots of the screen are normal and the characters take note of them. In the final shot, Charlie Brown is naked and Snoopy is hitting him with a piece of wood. Wonder what happened there.
Another example is in "How to Eat With Your Butt". They're sitting around having a conversation with Kenny's family, while in the background more and more people are crowding round the window to stare in and laugh.
In "Cartman Finds Love", Token and Nicole's Falling in Love Montage has Cartman watching them, happy that his racist notion that blacks should only date other blacks has come to fruition. One scene has him watching them very far away in the background.
At the end of "The List", Bebe reveals that she helped put Clyde at the top of the list to get free shoes, and shows off a pair that even excites Wendy. As the police are arresting Bebe, Wendy can be seen in the background stealing and admiring the shoes.
Superjail! is fond of these, especially in the second season, but they often turn out to be rather creepy, such as the monster eating its own guts, then its heart and finally dying.
In both "Rollercoaster" and its Musical Episode version, almost all the humor to the scene where Candace is talking on the phone with Stacy is all the random stuff going on in the background; Phineas and Ferb carry in trucks, lions, construction parts...
At the very end of the episode, just after the tree explodes. You can see the giant aluminium ball rolling in the background.
In "Last Train to Bustville," you can see Doofenshmirtz being chased by the dodo bird through the window in the room where Lawrence and Grandpa Clyde are just sitting.
In "The Magnificent Few," there's a sign that says "Egg laying contest this way."
In "Heart of Ice" as the reporter is finishing up on Mr. Freeze's latest crime, you can see several kids run up to the snow and start playing with it. A policeman chases them off, as this is a crime scene. However just as he shoos them away the kids pelt him with snowballs.
In "Mad Love", when we see Harlene Quinzel start her first day at Arkham, one of the patients (who looks suspiciously like Paul Dini) is casually licking the glass in his cell as she talks about her fascination with people who are mentally insane.
In "Almost Got 'Im", Poison Ivy inserts herself into the villain's card game after knocking down Killer Croc and swiping his chair. As the group continues their conversation, Croc can be seen throwing away another patron and taking his chair.
Made even funnier at the climax when it's revealed Croc is Batman in disguise, and the other patrons are all cops. "Uhh, sorry about this Commissioner..."
In the Sally Bollywood episode "The Return of Mr. Big", a science student points out that Doowee had garlic prawns for dinner several days ago. Then, (in the next shot) as Sally is talking to the science student a bit more, you can see Doowee (in the background) testing his breath, then gagging at the smell.
In another episode, after it's been revealed that Bob looted the lockers of two students, the two furious students proceed to chase him off, the chase subsequently continuing throughout the background of several other scenes through the episode... Until Bob and another culprit run smack into each other near the end.
At the end of the Transformers Prime episode "Convoy", after Optimus has stopped the train, you can see Miko punching Jack in the arm, then the pair giving each other a high-five.
The Boondocks: When Huey and Riley are among a group sent on a "scared stiff" program with Tom, the prisoners are always adding little comments (off screen) during what ever is being said:
Booty Warrior: See kids, when you go to prison, booty is the most important thing.
Random prisoner: Y'all better listen to him.
Prisoner: Shit man, I done raped a few niggas myself.
A green unicorn named "Lyra Heartstrings" is fond of this. Quite often in crowd scenes she will be jumping up and down ecstatically with a grin on her face, and it's common for her to do out-of-place human actions like sitting upright. In one memorable scene, she was seen in a city in the clouds, bouncing up and down. Despite the fact that she was a unicorn, they did not give her wings to make her a pegasus. In "Magic Duel" she appears in the background during the climactic fight calmly drinking a soda, uninterested in the battle.
In "Green Isn't Your Color", Pinkie Pie menacingly bites an apple while trying to scare Twilight out of telling Rarity's secret, only to really enjoy the apple and forget she was doing. During most of Twilight and Fluttershy's conversation following, Pinkie remains in the background still eating the apple.
In "Maud Pie": at the picnic, Maud takes a few bites of her sandwich, and then sets it down, and pushes her pet rock Boulder towards the food. The scene briefly switches to closeups where AJ offers Maud a muffin, but by the time the shot pulls back, the sandwich is gone and Boulder is all alone on the picnic blanket. No one seems to notice.
In "Trade Ya", whenever the episode cuts to one of the B-plots; Rarity and Applejack bickering over what to pool their resources to buy- Rainbow and Fluttershy can be seen passing in the background several times while on their Chain of Deals quest, carrying various items or struggling with the two-headed dog.
In "Twilight's Kingdom, Part 1", when Discord dresses up in a big, silly alicorn horn, wings, and crown, the Mane Cast all give him funny glances... except for Fluttershy, who appears to be giggling to herself.
In "The Cutie Map, Part 1", while the other ponies are talking to Double Diamond, Party Favor stares at Rarity, who looks uncomfortable.
In "Canterlot Boutique", during one of the scenes, one of the background ponies can be seen checking a price tag on one of the dresses, gawking, and hurriedly walking away.
Moral Orel has several of these, particularly on signs on labels. Notably, Reverend Putty's mug which reads "I Hate My Boss." Creator Dino Stamatopoulos talked about how he asked the animators to give more attention to these . . . which resulted in every shot featured the mug, even though it meant the mug was turned around in alternating shots.
In the VeggieTales episode "MacLarry and the Stinky Cheese Battle", in the scene where MacBob (played by Bob the Tomato) informs Chog Norrius that they were pranked by the Romans, Donald (played by Jerry Gourd) can be seen re-inflating the Whoopee Cushion that he accidentally sat on, throwing it back down, then sitting on it again, clearly looking like he is having way too much fun.
In the Mixels episode "Mixel Moon Madness", when the Nixels steal the food from the party, Niksput ends up hit in the head with Flamzer's volleyball in the background.
A verbal example in Steven Universe. While Steven and Pearl are having a serious discussion about Rose Quartz, in the background you can hear Garnet and Amethyst trying and failing to get a giant axe through the temple door.
Amethyst: Turn it clockwise! *loud crash* No, your other clockwise!
On Gravity Falls, this can happen even during very serious scenes. When Dipper and Mabel find the old newspaper in "Not What He Seems" that declares Stan to be dead, if you look closely or pause the scene while the newspaper is onscreen, you can see the article suddenly changes subject partway through; it goes from a serious (and plot-relevant) topic to how fashionable leg warmers are.
In other news, leg warmers are all the rage this week and we predict this style will go on forever.
In the episode "Mazes and Mutants" of Teenage Mutant Ninja Turtles (2012), while the Turtles are playing the titular RPG, Splinter walks past, casually opens the door, and receives a cheese-sicle from Ice Cream Kitty.
"Ultrahyperball" is about a game that's so complicated that nobody actually knows how to play; throughout the episode various unnamed players can be seen trying out weird strategies in the background. At one point, a player floats into the air and is then blown up for no discernible reason.
Toot & Puddle has one in "Free-Falling Friends" in which the squirrel sky-diving instructor, Webber, keeps approaching to enter the plane but gets blown back from the wind created by the engine due to it catching the bag with his parachute, while in the foreground, Puddle tells Toot that he's decided not to skydive. Webber finally solves the problem by packing the parachute in such a way that it can't catch the wind.
In the SpongeBob SquarePants episode "No Weenies Allowed", when Reg compliments SpongeBob for "destroying" Patrick without even touching him, Patrick can be seen still punching himself as if someone's punching him.