Ear Worm/Literature

Examples of Ear Worms in Literature include:

Older Than Radio: In 1876, Mark Twain wrote "A Literary Nightmare" (also published as "Punch, Brothers, Punch") about a jingle on punching train tickets getting stuck in his head.
This was the plot of a short story by Arthur C. Clarke, "The Ultimate Melody" in the collection Tales from the White Hart. A scientist noted the effect of Ear Worms in popular music, and determined to find the underlying rhythm that made them all so addictive through process of comparison and elimination. He apparently succeeded in touching on that "universal melody" for a moment, as the end of the story finds him completely vegetative, the song having matched so neatly with his brainwaves that it effectively locked them in stasis forever. As a note (no pun intended) of irony to the whole story, the machine that has been compiling and analysing these songs was turned off, still playing the ultimate melody, by a man who was completely unaffected by it. Why? He was completely, utterly tone-deaf.
The Sufficiently Advanced Aliens of Childhood's End by the same author use this as an example of precisely directed power. Yes, they could take out a dictator through armed combat, but it'd be much more effective and less destructive if they made it so there was a distracting little voice talking in his ear, 24 hours a day, that prevented him from thinking straight or planning his wickedness.
Alfred Bester's The Demolished Man features a man who wants to commit a murder in a world populated by telepaths. So he deliberately "infects" himself with an extremely catching earworm so that any telepaths won't be able to hear anything else that he's thinking. In-universe, earworms are referred to as "pepsis" although no one remembers why.
In one of her latter SERRATed Edge novels, one of Mercedes Lackey's protagonists manages to take down an entire group of psychics with the sheer Ear Worm potential of They Might Be Giants. Apparently, the fact that the band's songs are both A) incredibly catchy, and B) so nonsensical that you actually have to focus on the lyrics to keep up makes them a perfect block for any Mind Rapage. It definitely didn't help that Unseleighe psychics have absolutely No Sense of Humor, little comprehension of allegory, and the imaginations of lead bricks. They went positively insane trying to figure out what the hell the hero was thinking about.

"I know what the White Eagle is, but what in the name of creation is the Blue Canary?!"

The Terry Pratchett book Nation has an Ear Worm in the form of the Beer Song, described as a cheery little tune that bounces along and can't be removed from the brain with a chisel. It's important that the inhabitants remember it, though, as skipping a verse or two could result in fatal poisoning.
Discworld: The Hedgehog Song. It's an ear worm even though the words are never mentioned.
The story "Pie and Punch and You-Know-Whats", in Robert McCloskey's children's book Centerburg Tales, involves a record delivered by a mysterious stranger, which contains a song so catchy that the entire town ends up singing it. The only remedy is to get a different song stuck in their heads: "Punch, Brothers, Punch" from Twain's "A Literary Nightmare", mentioned above.
The short story "Rump-Titty-Titty-Tum-TAH-Tee" by Fritz Leiber concerns a rhythm and pattern of dots that form an Ear Worm so powerful that it essentially takes over the world, leaving almost everyone unable to do anything but obsess over it. Eventually, the spirit of a long-dead witch doctor gives the main characters an antidote (another Ear Worm which cancels it out), because, as the ghost explains, "it was starting to catch on down here, too."
In the Star Trek: The Next Generation novel Dark Mirror by Diane Duane, Deanna advises Picard to cultivate an Ear Worm in order to block her Mirror Universe counterpart's telepathy. He chooses George Strong's parody of "The Song of Hiawatha":

He killed the noble Mudjokivis.
Of the skin he made him mittens,
Made them with the fur side inside,
Made them with the skin side outside.
He, to get the warm side inside,
Put the inside skin side outside;
He to get the cold side outside
Put the warm side fur side inside.
That's why he put the fur side inside,
Why he put the skin side outside,
Why he turned them inside outside.

In the Dungeons & Dragons Forgotten Realms novel Finder's Bane, by Jeff Grubb and Kate Novak, the party is captured by the mind flayer god Ilsensine. To buy their release, they have to give it a song that it has never heard before. The minor deity Finder, in the party, gives it a recursive song—the last verse feeds into the first. The resulting Ear Worm gives Ilsensine big problems—so the mind flayer god ends up begging Finder to take the song away in return for three answers to questions.
China Mieville's short story "Wormword" features a deadly Ear Worm that can be spoken as well as sung. If you hear it intoned correctly, it causes a feedback loop in the brain that not only makes you recite the wormword over and over, potentially infecting other listeners, but also causes your brain proteins to distort, as if you've contracted a prionic brain disease.
Prose variant: in Dark Cities Underground, the protagonist once starred in a series of children's books his mother wrote when he was a boy. Even forty years later, he can't stop himself from mentally narrating his own actions in the catchy rhyming couplets his Mom's books used ("Jeremy Jerome Gerontius Jones, went to get an auto loan").
In The Name of the Wind the first book of The Kingkiller Chronicle, the protagonist Kvothe writes the song "Jackass, Jackass" to mock his school rival Ambrose. Since personally performing the song too often will get Kvothe in serious trouble with the University authorities, he writes the song as a deliberate Ear Worm. By the time he gets reported, it's all over town. Reader beware: the selections of the song included in the text are Ear Worms in their own right.
Poul Anderson's After Doomsday features a song, "The Battle of Brandobar", written to be a peculiar form of Ear Worm. The rhythm and rhyme of the song are carefully put together so it suffers little if any distortion when passed from singer to singer: "A space-hand who had never heard of Kandemir or Earth would still get their names correct when he sang what to him was just a lively drinking song. Only those precise vocables would sound right." This is essential, because the song is intended to let scattered Earthpeople know, "Hey, there's a bunch of Earthmen here."
Another Older Than Radio example is H H Munro, a.k.a Saki's "Cousin Teresa", in which a song containing the jaunty refrain "Cousin Teresa takes out Caesar, Fido, Jock, and the big borzoi." becomes an immense popular hit ("big-drum business on the two syllables of bor-zoi. It's immense."). The ensuing popularity of this absurd Ear Worm serves as a satire on the public obsession with trivia.
The Do-Da-De-Da-Da Code by Robert Rankin has a throw-away line in chapter 37 in a passage where everyone's fingers are poised for the last big number of a gig, "Fingers, Fingers, fingers. Fingers of Jonny's left hand on the neck of the wondrous guitar. Fingers of Andi Evans on the big buttons of the big recording equipment. Fingers of tom Gripping his drumsticks. Fingers of Gaz on the mic. A finger on the trigger. Two fingers of redeye from the optic. A finger of fudge is just enough." That last part is from the Cadbury's jingle that goes:

A finger of fudge is just enough to give your kids a treat.
A finger of fudge is just enough, until it's time to eat.
It's full of Cadbury's goodness, but very small and neat.
A finger of fudge is just enough to give your kids a treat.

In The Shattered Alliance book from the Magic the Gathering novels, Jodah the Archmage deters eavesdroppers at his study door with "a catchy little tune from my childhood that loops back on itself repeatedly." Since the spell makes people hear him singing it, another mage called it "cruel and unusual punishment."
Animorphs: The Yeerks are literal ear worms, except they crawl into your ear and take over your brain instead of being catchy. A more accurate version is how one Yeerk's host constantly recites Henry V in the back of his mind. It enrages the Yeerk so much that when it uncovers time travel, the first thing it does is try to go kill Henry V at Agincourt.
Audrey Wait is a book about an Break Up Song that also turns into an infamous Ear Worm worldwide, shaming all parties involved.