First of all, let me say that "shut up" is a terrible thing to say to anyone, and my children are certainly not allowed to say it, ever, and I do not say it. Very often.
But for some reason, people saying shut up can be as hysterically funny as people falling down and hurting themselves.
In chronological order:
1) When I was in college, my singing group went on a road trip to points South. One evening, when I was starting what turned out to be a doozy of a migraine, I was driving a minivan full of--if I may just be a traitor to my sex for a moment here--cackling hens on an unfamiliar Atlanta highway. At night. So when one of them asked jokingly,* "Are we there yet?" I replied, "No. Shut up." This struck everyone as very, very funny, and everyone in the group proceeded to say "No. Shut up." at the slightest provocation for the next year and a half, constantly reminding me of my moment of weakness.
2) The other day my father asked me a question that made me uncomfortable, and when I brushed it off my mother said, "Shut up, he explained." When I asked where that came from she said she thought Dashiell Hammett or Raymond Chandler, but the Internet later informed me that it was the genius Ring Lardner who coined this delightful bit of dialogue. I was particularly pleased since the incident in the book is so similar to my own experience.
3) Not long afterward I learned that King Juan Carlos of Spain had suggested to Hugo Chavez, "Why don't you shut up?" I had already felt a tenderness toward King Juan Carlos since this exchange on 30 Rock a few weeks ago: Steve Buscemi, the PI/fixer, suggests that Jack Donaghy quit his all-white country club, and Donaghy objects that it's not all white--what about "Johnny Carlos?" "He's the King of Spain. I don't think that counts." Now I love him passionately.
*This was supposed to be funny because I had already acquired my group nickname--"Mom." Talk about destiny, right?