Designated Hero: Parodied. Itchy is depicted as a hero and yet sadistically abuses and murders Scratchy in many ways, even if the latter did nothing to annoy him. Lampshaded by Homer at one point, too.
Designated Monkey: In a parody of standard cat and mouse cartoons, Scratchy is brutalized just because he's the cat.
Hilarious in Hindsight: In "The Tears of a Clone", Scratchy has died, and Itchy realizes that Victory Is Boring and life is meaningless without his Arch-Enemy around, so he creates a cloning machine and creates more clones of Scratchy so he can kill them. However, he grows tired because of the way the machine spits out clones, so Itchy creates a killing machine and makes an endless slaughterfest. Over fifteen years later, we get the Treehouse of Horror XXVI segment "Wanted: Dead, then Alive", whose plots became strikingly similar to "The Tears of a Clone", with Sideshow Bob as Itchy and Bart Simpson as Scratchy; the Reanimator in place of the cloning and killing machines; and a slightly different ending, which goes well with Bart and his family finally triumphing over Bob after all the ordeals the boy has gone through.