Basically, this is any child character explaining to his teacher why he hasn't done his homework. This will be either a lie, which may or may not be believed, or a Cassandra Truth. If it is the latter, expect them to also bring in the evidence proving their case (such as moist bits from homework, or even the animal itself.) The most common variant involves a dog, but other animals can be used as well.
Though this has become a Dead Horse Trope, and children rarely use this excuse seriously, the second variation on this trope is in fact Truth in Television. Many dogs do have a thing for paper, or are just Extreme Omnivores.
Someone from Harry's year in Oh God Not Again had to turn in their homework in tattered ruins, after the book Hagrid asigned for his class tried to eat it.
In Strange Visitors from Another Century one of Salazar Slytherin's students claimed that his pet bowtruckle ate his homework and Slytherin assigned him an essay on the importance of having a ready excuse.
In With a Forked Tongue I Lie in Wait (Taming Snakes) Harry started spinning an excuse about an "ugly monkey" in the lake and his missing Transfiguration essay and McGonagall replied "You don't honestly expect me to believe that a kappa ate your homework, do you?"
Mentioned in Thief of Time, in that no dog dares to eat homework given to Susan's students. Instead, they sniff it out and carefully bring it to her class if the kid forgot. She is like that.
In another Discworld book, it's mentioned that at Unseen University, your homework could eat the dog.
A Peanuts picture book has a literal version. Snoopy was playing WW1 Flying Ace and pretended Sally's book report was sensitive papers. She chased him and he swallowed the report. So she takes him to school the next day and takes him up in front of the class.
Sally: I might have a little trouble reading it. *shakes Snoopy* I SAID...I might have a little trouble reading it!
In the Raine Benares story The Trouble With Demons, a student tells his teacher that a Krog (A lesser demon that eats paper and ink) ate his homework. After a thorough quizzing from the teacher (Who is the head of the demonology department) on the alleged Krog, the excuse is accepted.
The main character in Paula Danziger's The Cat Ate My Gymsuit used the title statement as one of her excuses for not participating in PE class.
In one season 10 episode of M*A*S*H, Hawkeye gets in serious trouble because a goat ate the entire payroll (and, naturally, no one believes him; he is charged with stealing it). Later, Hawkeye is finally proved innocent when the goat subsequently eats a general's report on the issue. Seems sort of the same thing in spirit.
Briefly mentioned in an episode of Wizards of Waverly Place when the Russos adopt a dragon that's been transformed into a beagle. At one point, the dragon dog sets Alex's homework on fire, to which she comments: "The dog burned my homework, that's a new one."
In the Star Trek: Deep Space Nine episode "The Nagus", Nog tries to explain why he hasn't done his homework. The only excuse he comes up with is that "Vulcans stole his homework".
Ren Stevens in Even Stevens, when having to be paired up with a Pig, ended up having her homework eaten by the pig. She tries to explain this to her teacher, with predictable results.
An episode of Neds Declassified School Survival Guide involved Ned giving tips on good excuses. He comments that saying a dog ate your homework is a bad excuse... right before a dog eats his homework. The rest of the episode has him trying to find the dog and convince his teacher Mr. Sweeney that he wasn't lying.
Married... with Children invoked this trope in an episode where Peggy goes Back to School because she didn't pass home economics (no surprises there). At a scene, a teacher asks the class to wake Kelly, who quickly responded that her dog ate her homework. Later on, when Peggy is introduced to class, both her and Kelly fall asleep and the teacher asks the class to wake them both, who responded that the dog ate their homework.
And later, Al eats Peg's homework (a roast rack of lamb).
In one episode of Tattooed Teenage Alien Fighters From Beverly Hills, one of the heroes was doing her homework when they've been called into battle. She then took the homework with her, eventually leading to the homework being eaten by the monster. The teacher later sarcastically asked if a dog ate her homework. She answered it was a monster and the teacher took it for sarcasm.
Superhuman Samurai Syber-Squad had an episode titled "A Virus Ate My Homework". Unlike what the title might have made fans expect, Sam's homework wasn't eaten. His little sister painted it over. Fortunately, the emergency caused by the virus (namely, Kilokhan trying to use the world's nuclear arsenal to start World War III) made the students go home earlier, allowing Sam another day to redo the homework. It was cold comfort.
In an episode of Full House, the Tanners' newly-acquired puppy Comet eats DJ's book report, but DJ is Genre Savvy enough to know it won't fly even if it is the truth so she decides to tell her teacher Michelle ate it.
In one episode of TheWonderYears, Kevin has to do a school assignment involving a potato. His new dog eats it, and the teacher reacts in disbelief that his dog ate his homework.
Happens to the kid at the beginning of Motley Crue's video for "Smokin' In The Boys Room".
The Far Side: One cartoon has a class full of dogs with the teacher asking, "Well, here we go again... Did anyone here not eat his or her homework on the way to school?"
On FoxTrot, Jason's iguana Quincy has eaten his and his siblings' homework, causing them to either force Jason to fix up their homework (and it is also implied in the final panel that they were actually feeding the iguana their homework), or tell Jason off for feeding the iguana the wrong homework assignment. At least once Peter collected the bits of homework left by Quincy to take to his teacher to prove it actually happened.
In this strip◊ Garfield passes by a dog, who holds a sign saying: "Will eat homework for food".
In another strip◊, Jon goes to a class reunion, and meets his old English teacher, Mrs. Fronzak:
Jon: What are you doing at the class reunion?
Mrs. Fronzak: Waiting on that overdue term paper, Jonny.
Jon: My, uh, cat ate it!
Garfield: Leave me out of this!
Garfield also finds out that this is actually a very lucrative business for dogs.
Subverted in For Better or for Worse when Elizabeth tries to get Farley to eat her homework. He refuses to touch it.
Inverted in a cartoon published in a book of puzzles: a dog is ripping through a pile of papers, and a woman is screaming: "You stupid mutt! How am I supposed to tell my students that my dog ate their homework?"
Implied in Persona4, the main character can eat his little cousin science project. So it's easy to imagine poor Nanako trying to explain to the teacher that her cousin (or Big Bro, as she calls him) ate her science project...
In one strip, one of the other girls in class, on being asked about her homework, admits that she ate it herself. Specifically, Larisa put it through a blender and force-fed her the resulting mash. Nobody believes it, of course, but Sandra notices an electrical plug poking out of Larisa's backpack... and considering Larisa's nature, you really can't put it past her.
Larisa also once tries the excuse that her father ate her homework.
In one episode the dog really did eat Bart's homework just before he left for school. Naturally, his teacher didn't believe him.
"You ate my homework? I didn't know dogs really did that."
When the family dog, Santa's Little Helper, starts working for the police, Bart has no choice but to eat his own homework.
In an episode where Bart's teacher starts dating Ned Flanders and saw Santa's Little Helper, she asked Bart if that's the dog that eats his homework. Trying to convince her by giving the dog a homework for him to eat. The dog refuses. Bart then covers the homework with dog food. The dog ate the food, cleaned the paper and signaled the answer of a math question.
When Bart is nominated for class president and asked to give a speech, he says the dog ate his speech.
In Codename: Kids Next Door, Numbuh Five has a genuine problem of her homework getting eaten every day by a dog she passes by on the way to school. She has enough and decides to take the problem head on. Turns out that it's a rival classmate who can morph into a weredog and eats Five's homework out of spite, and the teacher is in on it, too. And, even then, it's only because Numbah Five has been helping Numbah Four with his homework (since he usually does poorly in school. This turns out to be useful for the KND because It turns out that poorly-done homework actually makes weredogs sick.
One short in What A Cartoon! Show has a cowboy telling his teacher his dog ate his homework. Obviously she doesn't believe him, but he tries to prove it by pulling out a dog chewing on a piece of loose-leaf paper. The teacher responds by lecturing him on bringing pets to class.
Kronk: Come on, "A llama ate my homework"? It's the oldest excuse on the book.
Yzma: Exactly! It's so old, no one will believe him.
Some children's homework fell victim to the Alaskan Bullworm on the corresponding Spongebob episode.
An episode of Catdog was devoted to the citizens of Nearburg making Dog eat their homework, which Cat exploits for their money. However, when the big one comes where Dog must eat the Mayor's written speech before he speaks up front, he becomes sick from eating too much homework, and Cat is forced to eat it himself. This turns out to be a bad decision as the entire crowd finds the idea of a cat eating homework ludicrous and boo the Mayor off the stage (and into the clowning business).
In one episode of Arthur, the Brain deliberately flouts several superstitions to show there is nothing in them, then has a terrible streak of bad luck, including having a dog eat his homework, which causes him extra distress because he knows how the report will be received.
In Animaniacs, this is a joke waiting to happen when the Warners attend school. Even when it was their first day. Turned out the dog was Wakko.
Teacher: Bad dog! Gimme that!
In Recess, TJ managed to have his teacher believe this showing his homework shredded and drooled (which was done by him and never started the assignment). She didn't believe it since he still had a scrap of paper on his lip.
In the same episode, Spinelli used the typical "dog ate it" response, and Vince claimed his brother ate it.
In Tales from the Crypt Keeper, there was a boy who, instead of using a dog, used a monster as an excuse. He told a homework-eating monster another monster showed up before. After a trip to monster land, the boy confessed and the monster took him home and made him do two homeworks: one to be eaten and another one to be taken to school.
Danger Mouse On The Orient Express: Penfold loses a valuable document to a hungry fish in a Venice canal. When he's captured by Greenback's agents he readily tells them that a fish ate the document. Nobody believes him.
An episode of Beverly Hills Teens is called The Dog Ate My Homework. In this case, the dog belongs to Bianca, and is sent by her deliberately in order to make Larke stay at home instead of competing against her. Also subverted, since for awhile, Larke's own cat is blamed, the homework was on a floppy, and there was no attempt to use the excuse.
One episode of Uncle Grandpa begins with the title character eating a boy's diorama of Ancient Egypt, which he needed to pass the class. Naturally, Uncle Grandpa tries to help, and naturally things go horribly wrong. Also naturally, the episode is called "Uncle Grandpa Ate My Homework."
Doug: When the kids are performing in the school talent show, Skeeter plans to play an ocarina he made out of one of the school cafeteria's dinner rolls. He's forced to withdraw from talent show when Roger's cat, Stinky, accidentally eats it. Mr. Dink doesn't believe him.
Mr. Dink: Not the old "cat ate my ocarina" excuse. At least be original.
Dennis the Menace and Gnasher: In "The Show Mustn't Go On", Dennis claims that he had to feed his homework to a giant paper-eating alien bug to prevent it from destroying Beanotown.
Many dogs like to chew on things and some find that textbooks and other homework actually are worth eating.
The adult party game Cards Against Humanity features a question regarding substituting 'dog' for something else. Naturally, given the nature of the game, this is very likely to enter the realm of Refuge in Audacity ...
This trope has been slowly replaced with "My printer broke" or "My email stopped working" in high schools.
A t-shirt available on Threadless features a x-ray of a dog. Inside the dog is a math book, a protractor, a pencil, and so on.