A gag in which a character orders food, then specifically asks that a certain ingredient be excluded: an ingredient that is not commonly found or ordered in that food to begin with.
A common use of this joke is with pizza and anchovies: Characters will specifically ask for "no anchovies" as if failing to do so would inevitably cause them to appear on the pizza — highly unlikely. Onions are another (un)popular choice, especially when ordering hamburgers.
Hatred for certain pizza toppings (or food additions) in general probably falls under Stock Yuck or Does Not Like Spam.
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In the Pokémon episode "Mystery at the Lighthouse", Brock tells Bill he is going to make hamburgers and asks if Bill wants one. Bill responds by asking Brock whether he "can cook without using tofu." Generally you would assume that if someone intends to make burgers, he is not going to use tofu.
Teenage Mutant Ninja Turtles (1990) has Michelangelo ordering a pizza near the beginning of the movie as Splinter talks about the "art of invisibility". As Splinter is finishing up his speech, Mikey is just about to finish the order, and he says, "Oh, but no anchovies, and I mean no anchovies. You put anchovies on this thing and you're in big trouble, okay?" right before Splinter throws a book at his head.
Rocky Rococo: Hello, I want to order some anchovies to go, and hold the pizza.
Parodied in Super Mario Bros. when President Koopa orders a pizza. "Hold the mammal."
In Amber Brown Is Not a Crayon, this is a Running Gag between Amber and Justin. They always ask for a pizza, "hold the anchovies," and then laugh at the mental image of the pizza boy holding an armful of anchovies.
Reginald Brooks:[ordering pizza for his hostages] I want 10 with sausage, 10 with pepperonis. And no anchovies. I see one anchovy and I kill the librarian.
Friends episode "The One the Morning After" when Rachel is very pissed off with Ross:
Rachel: Yes, I'd like to order a large pizza. Ross: No anchovies. Rachel: With, uh, extra anchovies. Ross: That's okay, I'll just pick 'em off. Rachel: Yeah, and could you please chop some up and just put it right there in the sauce?
On Supernatural, there was a version involving not anchovies, but a vampire who was worried that he may have had unsolicited garlic put on his pizza. It lampshaded the unrealisticness of someone who worries about unsolicited anchovies, garlic, or such toppings with the delivery guy's reaction: He impatiently asked, "Did you order any garlic? Then no, there isn't any." A bit more justified than some cases, though it would be more so if he'd demanded to know if there was garlic in the sauce.
ALF once ordered a pizza with everything except beets. He specified clearly that he did not want beets.
Tom Smith's "Domino Death" references this with adding "no anchovies, please" as one of the many offenses that will garner your death at the hands of the psycho narrator.
The Firesign Theatre: George Tirebiter tries to order "a pizza to go, and no anchovies" from a place called Nick's. Unfortunately for him, George has the wrong Nick on the line:
"No anchovies? You've got the wrong man. I spell my name...Danger!"
In the ClueFinders book "The Mystery of Microsneezia", Leslie's preference for broccoli is treated this way by the boys though in Real Life, broccoli is merely an uncommon topping, not an unpopular one and is fairly easily found in the California area where the Clue Finders are implied to live.
A joke about Jean-Paul Sartre goes that whilst working at a café he asks the waitress for a coffee, no cream. The waitress replies that they are out of cream, how about a coffee with no milk?
A non-food variant appears on the famous Morecambe and Wise skit with Andre Previn. Explaining the "special arrangement" of Grieg's piano concerto, Eric says, "easy on the trombones".
In the Looney Tunes short "A Hound for Trouble", Charlie Dog attends to a customer at a restaurant in Italy, who orders spaghetti with "no onionza".
The Silly Symphony "The Golden Touch" has King Midas, desperate to lose the golden touch lest he die of starvation, bargains with the elf who gave it to him "my kindgom for a hamburger sandwich!" The elf sardonically asks "With or without onions?" After taking back the golden touch and all of Midas' worldly possessions, a hamburger materializes. Midas, nevertheless, is overjoyed that it has onions.
No Anchovies, Least Common Pizza Topping, Hold The Nonstandard Ingredient