BT from .hack//Sign named her character based on the removal of this from her favorite food. I'll give you a hint. It's not Bacon and it's not Tomatoes. Mimiru points out it has no taste upon being informed of this which leaves her bewildered as to why BT dislikes it.
Sailor Moon: Each of the Sailor Senshi have a least favorite food listed in their profile. Usagi's is, ironically, carrots.
Crayon Shin Chan: Shin-chan hates green peppers. Possibly the reason why he always asks older girls if they like them is to allow him to keep hitting on them.
Similar to Sailor Moon, most of the cast of Naruto has a food they dislike, with the exception of Lee, who cannot dislike any kind of food. Naruto in particular hates vegetables, and a brief flashback shows Kakashi appearing in his window to offer him some vegetables with his ramen.
The captains and lieutenants of Bleach have their favorite foods listed in their profiles, along with foods they dislike. Gin likes persimmons and dislikes dried potatoes (because he bit into one thinking it was a persimmon), while interestingly enough, his lieutenant Izuru dislikes persimmons. Komamura, an anthropomorphic wolf, has hated carrots ever since his father told him that they don't eat them.
Kanako Urashima in Love Hina doesn't like sweets at all. Naturally, she was adopted into a family of confectioners, and she crushes on her adopted brother, who is an expert even amongst the family at them.
Akisame Koetsuji of Kenichi: The Mightiest Disciple loathes bell peppers to the point that they're occasionally used as a threat for dinner if he doesn't do something or other. He always complies.
Yang Wen-li in Legend of Galactic Heroes dislikes coffee very much, to the point that during the prequels when he was choking over some food and was saved by a cup of coffee offered by his future adjutant and wife Frederica Greenhill, the first thing he said was "I hate coffee. I wish you'd given me tea instead."
In Not Your Usual Veela Mate after Dumbledore arrempted to excuse a Slytherin student who cast the Cruciatus Curse on Harry, a portrait of Godric Gryffindor ordered the elves to serve him all of his least favorite foods: liver, haggis, bubble and squeak, kippers and boiled cabbage.
King Verence detests custard, after having it dumped on him many a time during his youth in the Jesters' Guild. (It probably doesn't help that there's a custard actually called a fool.) He detests it so much that there's a national ban on custard in Lancre.
Makepeace Thomas Bounder, "The Poet of the Cabbages" in The Discworld Almanack, wrote a treatise on "The Hellish Root," aka the potato, believing its popularity to be directly responsible for people being uninterested in cabbages.
When first introduced in the series, Cohen the Barbarian hates soup of any kind. This is because his teeth have fallen out and dentures are unknown outside of Agatea at the time, meaning the only food he can actually eat any more is soup and mushed veggies, and so well-meaning people offer him dozens of different kinds of (and recipes for) soup. He stops grumbling about it later in the series because by then he has pure diamond dentures, meaning he can eat anything he wants to eat again.
In one of the short stories in Marcovaldo by Italo Calvino, Marcovaldo develops an absolute loathing for sausage after eating it every day for weeks.
Dr. Seuss's "Green Eggs and Ham"—The protagonist spends most of the book declaring how much he dislikes it, though by the end he is persuaded to try it and discovers that it's actually quite good.
Pumuckl, the kobold protagonist of a German children's series hates cheese (which he calls "foul milk").
Harry Potter: Dumbledore, despite his general fondness for sweets, avoids Berty Bott's Every-Flavor-Beans after coming across a vomit-flavored one in his youth. He tries them again at the end of the first book, and...
"But I think I'll be safe with a nice toffee, don't you?" (eats bean) "Alas. Earwax."
Bones: Brennan doesn't like pie, at least fruit pie, because she doesn't like cooked fruit.
Parks and Recreation features an entire town who dislike vegetables and salad. There was one business named "Sue's Salads" that was actively hated on be Leslie Knope, who is an otherwise cheerful person, and it went bankrupt in the course of a season. Ron Swanson exemplifies the trope, he also dislikes fruit (he can't bring himself to eat a banana until he smooshes it into a giant beef burger), diet versions of normal food or drink like skim-milk, dislikes fish (claiming it is close enough to a vegetable) and invented the 'turf and turf' which is two giant steaks served side by side.
Newman on Seinfeld hates broccoli, calling it a "vile weed". Of course, it seems he probably hates all vegetables.
In the American version of Big Brother, seasons 7 and beyond introduced the diet called Slop. The food is a mushy food that contains a lot of vitamins and proteins, and the contestants regularly express their dislike for being "Stuck on slop" and compete as hard as they can to not be the side that is forced to eat nothing but slop for a week. It is actually designed that way on purpose...as the Peanut Butter and Jelly diet would make people sleep all the time...the Slop would have people awake for more drama and encourage people to play harder during the food competitions.
Red Dwarf Dave Lister hates Pot Noodles to the point of eating dog food instead when they're his only options. When stuck on a version of the ship that's supposedly the "higher" version, he orders a Pot Noodle to see if it can make them any good. It does, and he's amazed.
Sarah Jane Smith Doctor Who and The Sarah Jane Adventures hates ginger pop. It's how the Doctor recognizes her ginger pop-drinking android impostor in "The Android Invasion.''
The Seventh Doctor loathed pears. The Eleventh turns out, after much experimentation, to hate apples, yogurt, baked beans, bacon, and bread and butter. To be fair, he had just regenerated.
There's a clip cut out of "Human Nature" that says that the Tenth also disliked pears, and didn't want Martha to let him eat them while human. You still see him doing just that - John Smith really got on Martha's nerves after a while.
Bizarre Foods With Andrew Zimmern: Andrew will cheerfully eat almost anything: bloody entrails, duck eggs with a fetus inside, pig brains preserved in aspic, etc. But in an episode about Hawaii, he was presented with a dish made of spam and could barely force himself to taste it. He even went on for about five minutes about how much he hates spam. He also has a strong aversion to durian. He also does not like walnuts. When Zimmern guest starred on the Minneapolis episode of Man v. Food, he had host Adam Richman (who makes his living eating enormous amounts of fatty, sugary, and/or unearthily spicy foods) try some lutefisk. He couldn't stomach more than one bite.
Andrew Zimmern: Mmmm. That's some good lutefisk.
Adam Richman: (face contorted in disgust) How can you tell?
Anya from Buffy the Vampire Slayer explaining alternative universes, bearing in mind that her example is bound to be self-centered: "Suppose you don't like shrimp. Well, blahh, you say, I wish there was a world without shrimp." This is in addition to bunnies of course.
In an episode of Mighty Morphin' Power Rangers, the heroes discover that the current Monster of the Week, the Pudgy Pig, who was at first believed to be an Extreme Omnivore, has a dislike for spicy food. After tricking him to eating some hot peppers, it appears that he's actually somewhat allergic to such food, and they defeat him easily.
In one episode of The West Wing, Charlie is asked by a reporter if there are any foods the President doesn't like. He answers (truthfully) that the President doesn't like green beans. This gets him in trouble, because it's an election year, and the staff is afraid it might put off green bean farmers. (This may be based on the George H.W. Bush example in Real Life, below.)
Hornblower: Lieutenant Bush owns he had to eat turnips as a boy, but he never touches them now.
Throughout the series, there are food items that are absolutely loathed by certain characters. Natalie from Island Of Happiness is Squicked by mushrooms and Julia (same game) feels the same about fish.
In Tales of Symphonia, every character has a least favorite food as a game mechanic. The most notably overblown in fandom terms is Kratos's (not that one) hatred of tomatoes, possibly because it's amusing for such a stoicBadass to have that kind of a weakness. Notably there is one who shares his dislike his son.
In fact, every player character from the Tales Series (with the exceptions of Anise and Yuri) has a least favorite food; some games even have a mechanical display of this (such as said food having less of an effect, or even the opposite effect, on said character).
Genis Sage doesn't care much for Gels (the healing items of the game), if you don't give him any for so long, he gets the title "I hate gels!" and a skit.
Flynn's dislike of squid in Tales of Vesperia is another popular fandom topic, particularly on the Japanese end, which is often Flanderized into him having a full blown phobia of the creatures.
A similar example are the Man-Eating Plants in Luigi's Mansion: Dark Moon. They aren't ghosts, and are thus immune to the Strobulb and Poltergeist 5000, but Luigi can defeat them by force-feeding them a spikey fruit that often grows nearby. Luigi can use a cooked chicken in place of the fruit to defeat one particular Plant in the Treacherous Mansion, which also gains him a Diamond.
Grunt from Mass Effect 2 is almost the ultimate example of an Extreme Omnivore - the smell of burning plague victims makes him hungry. However, he hates ramen (it looks like worms, apparently).
BlazBlue: "There are two things in this world that I just can not stand! Lies and evil and lies and...BELL PEPPERS!"
Your character in Final Fantasy: Crystal Chronicles starts out with at least two foods they don't like. These don't restore a lot of their health, though if you feed them those foods often enough they'll start to like them.
Dragon Age II: Fenris apparently hates fish, according to one of his comments when entering a warehouse for a quest.
Then again, this might be because of the smell.
In Sonic Unleashed, Sonic gains EXP from foods he eats, with the amount of EXP he gets based on how much he likes the food. He generally doesn't seem generally fond towards basic sweets and drinks, and seems to have a strong distate for seafood.
It's heavily implied that GLaDOSreally hates potatoes by the end of Portal 2.
Unlike Flint, who LOVES cheese, Kumatora and Boney of MOTHER 3 hate it, and will recover less hitpoints from eating it.
Starting in the third-generation games, most Pokémon have a preferred flavor and a disliked flavor, depending on their nature and corresponding to the stats improved/reduced by their nature. If fed Pokeblocks or Poffins of a disliked taste, the Pokemon will gain less benefit, and certain healing berries will inflict confusion if the Pokemon doesn't like how they taste.
Saber from Fate/stay night is well known for her large and nondiscriminatory appetite. However, she does not like octopus. At all. Not so much for the taste as the appearance; upon finding out that a food she did enjoy (takoyaki) was stuffed with fried octopus, she expressed horror that she'd been eating 'demonic fish of the underworld'. This is revealed elsewhere to be due to her confrontations with the Fourth War's Caster in Fate/Zero, who literally did try to kill her with summoned demonic fish of the underworld; the entire experience left her with a dislike for tentacled, squishy things.
In Higurashi no Naku Koro ni, Shion doesn't like canned meat, Satako doesn't like pumpkins, and Hanyuu doesn't like spicy food and wine.
Da Capo II: Minatsu Akasame is a robot who requires regularly eating bananas in order to keep functioning. She doesn't like them at all.
Homestuck starts on John Egbert's birthday. As a result of all the cake he has been eating for the occasion, he is sick to death of baked goods — especially those by Betty Crocker. This nearly causes a Heroic B So D when he realizes that his beloved Fruit Gushers are made by the "Heinous Batterwitch," but he decides that angsting over it is stupid.
It's implied that his hatred of Betty Crocker products goes back much farther than that, since his adoptive great-grandmother was Betty Crocker herself and baking seems to be something his father does constantly regardless of the occasion, or lack thereof.
In the Alpha Session, John's counterpart, Jane Crocker, dislikes Fruit Gushers, ironically enough.
Haley in The Order of the Stick doesn't like pickles, leading her none-too-bright rival Crystal to think she can kill Haley by pelting her with pickles.
That's hardly part of this trope, as not liking babies is quite common. Remember that Mit D never said to like human flesh, it's just that Xykon assumed that a monster should eat babies.
Played for Drama with Kokkan in "A Broken Winter". After a year as a child spent around freshly slaughtered animals and dead bodies in Irihi slaughterhouse, he refuses to eat meat of any sort. It's also one of the signs of his ongoing battle with PTSD.
In Webcomic/Waterworks, Tubs does 'not 'like fish. Even the smell will keep him out of an area.
In The Autobiography of Jane Eyre, Grace Poole says that Mr Rochester has a mind aversion to uncooked tomatoes. Grace herself is somewhat obsessed with food and wouldn't dare to touch anything with glutens.
Tohru's dislike for fish is a constant thorn in his side in Jackie Chan Adventures. This may have had to do with a Running Gag where he was often defeated by fish used as an impromptu weapon before his Heel-Face Turn, though he is shown to actually dislike it as food as well.
Angelica of Rugrats loves all cookies except coconut ones.
In Codename: Kids Next Door, Father hates broccoli. In fact, he claims that everyone hates it, and that the reason adults make kids eat it is so that they won't have to. The stuff is downright poison to KND Operatives. Numbuh 362 eats her way through a wall of broccoli to confront him, and while she manages to triumph and save the day, it sends her into a two-week coma afterwards.
One episode of The Real Ghostbusters featured a man who hated chicken so much he wished all chickens out of existence. The demon he made the wish to was so embarrassed by having to carry out such a ridiculous task he actually teamed up with the Ghostbusters just to have it undone.
In one episode, Binky the Clown reveals that he hates mayonaise.
One episode had Garfield complaining about anchovies in his pizza - but he does like it in the comics.
In Code Lyoko, Odd is a Big Eater who'll eat almost anything. He doesn't like sushi, however, telling Yumi's mom that he "didn't care for" it in one episode where she offered it.
Mighty Rai from Hero108 hates bananas. Unfortunately, they're the source of his electric powers, so he has to suffer them.
Young children tend to have a distaste for bitter flavours in general, and more sensitive tastebuds into the bargain. Hence the famous dislike of vegetables, particularly sulfurous ones like cabbage and spinach. People generally grow out of this as they get older, but by then many of us have built up a psychological dislike of said vegetables because we associate them with all those dinnertime arguments. It doesn't help that many people don't know how to cook them properly, either.
George HW Bush: "I do not like broccoli. And I haven't liked it since I was a little kid and my mother made me eat it. And I'm President of the United States and I'm not going to eat any more broccoli." Broccoli farmers sent 20,000 pounds of broccoli to the White House in protest. We're guessing he didn't eat it.
Pythagoras (of Pythagorean Theorem fame) was known for his hatred of beans. To wit, Pythagoreanism was a religion based off his work and philosophy, and beans were verboten in said religion, deemed "unclean." Pythagoreans didn't eat beans not because they deemed them unclean, it was exactly the other way round. They believed in reincarnation, and by their books beans were the main target for human soul to reincarnate into. Thus eating beans was, for Pythagoreans, something too close to cannibalism.
People who grow up poor enough to eat certain foods constantly will often avoid them once they get enough money for a varied diet. That's the basis for the whole family of so called "poverty foods".
H. P. Lovecraft was allergic to seafood. This explains the cephalopoidic and piscine nature of a great many of his monsters. It probably didn't help that he lived in New England, where seafood can be a little hard to avoid.
People with Asperger's Syndrome, and other types of autism, tend to have hypersensitive taste buds and/or stomachs, hence they may have a strong aversion to certain types of taste or textures.