Autocannibalism: In one short, Itchy (disguised as a restaurant employee) serves Scratchy his own belly. The unknowing Scratchy's attempt at eating it only results in the bits of it he swallows popping back out of a hole cut in it.
In the show's history, early cartoons were fairly routine. In their first appearance – in a Tracey Ullman-era short called "The Bart Simpson Show" – Itchy places a firecracker in Scratchy's mouth; in their first series' appearance (Season 1's "There's No Disgrace Like Home"), the show is simply another "place a bomb in Itchy's mouth and watch the explosion" cartoon. Future cartoons would be more detailed.
Add to that in both cartoons, Scratchy actually started the feud chasing Itchy like a traditional cat and mouse cartoon. Episodes afterwards skipped the formalities and just started with Itchy brutalizing Scratchy for kicks.
In-universe, "Manhattan Madness", a cartoon created entirely by Chester J. Lampwick, only features Itchy and had him visiting Manhattan to attack people. "That Happy Cat", meanwhile, is a solo Scratchy effort by Roger Myers Sr. with no plot whatsoever. Then Myers stole Itchy and his formula and used them in "Steamboat Itchy", and the rest is history.
Enemy Mine: The duo brutalized Hitler in one war time cartoon (before Itchy double crossed Scratchy and decapitated him too). Another has them team up against an annoying blue haired squirrel berating their antics (see Take That).
Karma Houdini: Itchy, who never receives any punishment for his brutal and unprovoked attacks on Scratchy (except for one episode).
Lighter and Softer: After Marge's crusade to tone down the show's violence succeeded, the show went through a phase invoking this trope.
Moral Myopia: Itchy constantly abuses, torments, mutilates, and murders Scratchy and enjoys it all the while. But if someone else takes enjoyment out of watching Scratchy be in pain, he gets all up in arms.
The Movie: In-story, the show had a movie released in theaters and either had a sequel or rerelease at the start of The Simpsons Movie.
Mr. Alt Disney: Itchy and Scratchy's inventornote well, Scratchy's inventor at least, Roger Myers Sr, is a thinly disguised spoof of Walt Disney with his theme park and the urban legends surrounding his antisemitism and being cryogenically frozen after his death.
Oh, Crap: Several shorts have Scratchy seeing his impending doom coming, and screaming in terror as he hopelessly tries to avoid it.
Older than Television: Older Than Radio, even. the Ur Example being honoured is George Herriman's newspaper cartoon dating from 1913, Krazy Kat, syndicated nationally and revolving around the titular Krazy, a cat who is forever on the receiving end of flying bricks from a sadistic mouse called Ignatz.
The concept may even be much, much, Older Than Steam: there are Egyptian drawings from 3,000 years ago showing mice enthroned as Pharoah receiving tribute from subservient cats. One drawing shows a mouse-Pharoah ordering the death of a cat-serf who has displeased him. Or her.
Overly-Long Tongue: Scratchy's isn't so much long as stretchy; at one point it gets tied to a rocket which reaches the moon before Scratchy even notices.
Re Tool: Into a Lighter and Softer show. It was changed back when Marge Simpson, who started the protests against the show's violence, had a wholly different opinion on Michelangelo's David (which was on a coast-to-coast tour of the United States at the time) from the rest of the protesters.
The first cartoon in 1928, "That Happy Cat" only showed Scratchy walking down the street and whistling. Unsurprisingly, it wasn't a success, and the series only caught on when Itchy and violence were added (read: stolen from Chester J. Lampwick).
Shoo Out the New Guy: A character named "Poochie", voiced by Homer, was introduced, gelled horribly with the show, and was dumped hastily out of the show.
Shoot The Television: The short "Little Barbershop of Horrors", "written" by Abraham Simpson, ends with Scratchy's head (now just a skull) going through a ceiling and into Elvis Presley's television set. Elvis promptly produces a revolver and shoots Scratchy's skull through the TV.note Referring to an incident where Elvis shot a TV set in his hotel room, supposedly when Robert Goulet appeared on-screen. Depending on the teller, Elvis was mad at Goulet dating one of his backup singers, didn't like Goulet's singing, or just plain had an Ax-Crazy moment.
Elvis: Aww, this show ain't no good! *BANG!*
Shout-Out: Many, to various classic cartoons. A notable one is Itchy having the subtitle of The Lucky Mouse in his first, lost cartoon, referring of course to Oswald the Lucky Rabbit
Take That: In response to Marge Simpson's protests on the show, there was an episode featuring a squirrel with Marge's blueBeehive Hairdo trying to break off Itchy and Scratchy's fighting... only to get killed by them.
Also, the I&S cartoon at the beginning of The Simpsons Movie has Itchy nuking the moon with missiles; the most extreme option is listed as "accidental bombing", with "accidental" in quotation marks.
Roger Myers Sr is a very unflattering portrayal of Walt Disney. The backstory of the I&S studio is a mishmash of conspiracy theories about the Disney Company.
Team Rocket Wins: The 'lost' episode where Scrachy finally gets revenge on Itchy by running him down with a combine harvester.
A storyboarded episode had Itchy steal Scratchy's pie, so Scratchy threw him in a vat of acid. Unfortunately, this was during a massive censorship push, so if they went with Marge's suggestion, Itchy would have shared the pie. Which he stole.
"Burning Down The Mouse" is apparently the only aired episode where Scratchy wins, by blowing Itchy up with a large arsenal of explosives. Unfortunately, the viewers never get to see the end, because one of Homer's college roommates who are crashing at his house unplugs the TV and doesn't plug it back in until it's over, where the TV just turns back on in time to see a huge mushroom cloud and "The End" superimposed over the shot (followed by Krusty declaring that "They'll never let us air that again! Not in a million years!").
A Taste Of Defeat: Another episode still had Itchy kill Scratchy, but lost as well, having set up the prank for so long that when it's over the aged Itchy dies of a heart attack laughing too hard.