Lisa: And now, you can be a normal kid, instead of a one-dimensional character with a stupid catchphrase. [Lamp breaks] Homer: D'oh! Bart: ¡Ay, caramba! Marge: [murmurs] Maggie [suck suck suck] Flanders: Hidely-ho! Barney: [belches] Nelson: Haw-haw! Mr. Burns: Excellent! [Beat as everyone looks at Lisa] Lisa: If anyone needs me, I'll be in my room. [Lisa walks up the stairs to her room] Homer: What kind of catchphrase is that? — Bart Gets Famous
Nearly every character who has appeared more than ten times has at least one, with the notable exception of Lisa. The writers and producers of The Simpsons deliberately changed Bart's catchphrase on a regular basis, even going so far as to do a Lampshade Hanging about it in one episode (where Bart becomes famous for his catchphrase "I didn't do it", and that ends with a long sequence of characters spouting their catchphrase, ending with all of them staring expectantly at Lisa, who has no catchphrase and goes to her room in a huff.
Also, parodied in The Simpsons' "Homer to the Max" episode, in which a TV cop, also named Homer Simpson, has the catch phrase "And that's the end of that chapter." When he was reworked to be a clumsy oaf, his catchphrase became "Uh-oh, Spaghetti-os!"
The changing of Bart's catchphrases was lampshaded a couple of times - in "The Summer of 4' 2" Bart complains to Marge that Lisa became popular by copying him, just as she says "Don't have a cow, man". Marge replies "You haven't said that in four years. Let Lisa have it." And in "Skinner's Sense of Snow", Bart reads "Underachiever and proud of it" in his permanent record and asks "How old is this thing?"
Bart Simpson: "Eat my shorts", "Don't have a cow, man", "Ay Caramba", (when introducing himself) I'm Bart Simpson, who the hell are you?
Homer Simpson: "D'oh!", "Woo-hoo", "Mmmm... [x food (usually donuts)]", "Why, you little—!", (spotting something that interests him) "Ooh!", (disappointed) "Oh! or Aw!", "The Simpsons are going to [location]!", "Stupid Flanders!", "AAAHH!!!"
Marge Simpson: "Hrmmm"
Maggie Simpson: her "sucking pacifier" sound
Mr. Burns: "Excellent", "You're fired", "Release the hounds", "Simpson, eh?"
Smithers: "Sir", "That's, uh, Homer Simpson, sir, one of your [insulting term]s from sector 7-G".
Barney Gumble: his belch
Krusty: "Hey Hey (laugh)", "Uuuuggggh"
Apu: "Thank you, come again."
Ned Flanders: "Hidely-ho, neighborino", "Okelly dokelly", "Diddly!"