In Plautus's plays, table-companions (a peculiar Roman institution, also called "parasites") are played as comically large eaters, making this Older Than Feudalism. Ergasilus in Captivi, given the run of Hegio's kitchen, causes an uproar not unlike those common in The Slayers.
Mr. Croup likes words, while Mr. Vandemar is always hungry.
Miles Teg from Heretics of Dune undergoes a transformation that unlocks his Super Speed powers, and as a consequence, has to consume many, many normal human portions to satisfy his hunger. Justified as his metabolism is accelerated to compensate for the increased energy demands. This is commented upon with amazement by the people who observe him eat.
The Hungry Tiger in the Land of Oz books is quite possibly the largest and most powerful tiger in the whole of Nonestica, and has an appetite to match. He is only full once — after devouring a good portion of a royal banquet.
Everyone likes to eat in Redwall, but hares have it as a defining trait. To great comedic effect in most of the books. There's also a sequence in Salamandastron where two runaway Mooks try to keep up with the Abbeydwellers' eating, but since they're not used to eating so much, they make themselves horribly ill and have to be given a "fizzick" which makes them bring it back up.
Causes something of a problem in another book; a horde of squirrels has agreed to help a hare find his platoon, but, in order, he:
Comes dangerously close to overeating on a piece of the squirrels' waybread, one bite of which is dense and calorie-filled enough to last a squirrel all day
Promises three entire loaves of the stuff to an owl they're bartering for info with, when they could have haggled him down to one had the hare not been so desperate.
Bitches, moans, and in general makes a whiny nuisance of himself over how hungry he is when the squirrels decide that since it was his bright idea to give three loaves to the owl, he can be one of the three poor schmucks who goes hungry until they can make more.
And finally, gorges himself on unripe apples, forcing the squirrels to give him a dose of their own brand of "fizzik" before they can move on.
Bescarum the hare in Triss is also this. It gets him in trouble on more than one occasion, once when he eats all of the food of a tribe of hedgehogs that had given him and his friends shelter for a while. Had his badger friend not bailed him out the hedgehogs would have had him work to pay back the food he ate. He later does it again in Redwall, eating a massive trifle that was supposed to be the prize for the winner of a race the Dibbuns were having. He's not bailed out this time, and is punished by being forced to scrub the Abbey from top to bottom while eating nothing but a single meal of lettuce and water. In a stunning case of Never My Fault he runs away rather than face the music, and sets up the final conflict of the book.
The hobbits from The Lord of the Rings are seen as able to put away large quantities of food. In a normal day, they eat at least seven meals (Breakfast, Second Breakfast, Elevenses, Luncheon, Afternoon Tea, Dinner, Supper, plus whatever snacks they can sneak between); The Hobbit states it's eleven meals a day. As a reference to this, in the Films, elvish Lembas bread, a small bite of which is supposed to feed a normal man, is consumed in the amount of several loaves each by the sidekicks Merry and Pippin, with only mild indigestion to show for it.
In the book, though, it is Gimli who inadvertently eats a day's worth of lembas, having mistaken it for the much less appealing cram (human-made waybread with excellent keeping qualities and the flavour and texture of cheap cardboard) and reacting with delight on finding that it's tastier than the best honey-cakes he knows of.
From the Wild Cards series of novels, we have Croyd "The Sleeper" Crenson, who can sleep for as little as a night or as much as several weeks/months. Upon waking, he is always a Big Eater, to the point that there's a jingle about it (Sleeper waking, meals taking/Sleeper speeding, people bleeding), and people recognize him by his eating habits.
Croyd is the most obvious example, but it's mentioned once that the Great and Powerful Turtle has to eat fairly constantly, as using his telekinesis drains his physical energy, and it is implied that the other aces also have a faster metabolism to fuel their abilities. The most prominent example is the Midnight Angel, who is mentioned in her appearances as being constantly hungry due to her highly enhanced metabolism, and is capable of downing meals that shock the waitresses (or is at least constantly eating).
Tales of MU has the burrow gnomes with eating habits inspired by the above-mentioned Hobbits, as well as Mariel the sylph who eats as much as four people in order to keep her hyper metabolism up.
All the bird-kids in the Maximum Ride series have this, because of super-high metabolism to give them energy to fly. Amusingly, in the first young adult novel, they show up at a restaurant and start to order dinner, and the staff think it's some sort of prank.
Most of the Brotherhood boys in J.R. Ward's Black Dagger Brotherhood series. Like Rhage (who is regularly described or insinuated to be the biggest eater, even amongst the brothers) and Zsadist, as of book 3, Lover Awakened. The latter is an especially fortunate development since the extreme and very detrimental opposite was the case beforehand. In layman's terms, Z more than half starved himself for over a century, hating and outright not trusting any and all food he couldn't see whole or make himself, since he "didn't know if it was tampered with" otherwise. But thanks to his bonding with the aristocrat vampire Bella, he's since done a 180 and adopted eating alongside Rhage.
Templeton the rat in Charlotte's Web might be a Villainous Glutton if he actually did anything truly malicious (he's stated to have "no morals") but bribing him with food is pretty much the only way to get him to help with anything. He's persuaded to go to the county fair after being told of all the discarded food that would be on the ground after hours, and eats so much then that he comes back the next morning bloated to almost twice his size. Later in the book, after Orson promises to let him eat first from his slops after helping save Charlotte's egg sac, he grows to nearly the size of a hedgehog from eating so much.
Claudia Kishi from The Babysitters Club 1990s-era juvenile book series is a model-thin junk food addict. Many an eating disorder can be traced to this character.
Fitz Kreiner from the Doctor WhoEighth Doctor Adventures. He also has Extreme Omnivore tendencies, and questionable table manners. And, as per usual for this trope, he's incredibly skinny, although when he's not busy running for his life and can have three square meals a day, he doesn't take long to get a bit out of shape. Fridge Brilliance: it's probably because by the time he's 33, he's spent about 2/3 of his life either under rationing or traveling with the Doctor. Being on a see-food diet (you know, if he sees food, he eats it) is ordinarily a useful survival mechanism which he probably picked up when he was still a small child.
The Librarian in the "Hard-Boiled Wonderland" segment of Haruki Murakami's Hard-Boiled Wonderland and the End of the World is one of these, to the point where most of her salary is used to pay for food. It is explained as an effect of her gastric dilation.
Honor Harrington's portions often get comments (and envious stares from her less metabolically blessed colleagues), but then she is a genetically engineered heavyworlder with a Super Strength and requisite metabolism. Though, given how much exercise she subjects herself to, she probably wouldn't be fat even without her genetic tweaks.
Her big eating was even deconstructed in In Enemy Hands, when she was captured and she lost a significant amount of weight because she was only fed standard rations. Her warden was particularly frustrated by this since he was trying to break Harrington psychologically but needed her physically fit for propaganda footage.
The Dresden Files: Harry Dresden says that he "eats like a horse", but is still tall and skinny, because he actually alternates between eating like a horse, and getting so wrapped up in what he's doing that he forgets to eat. So it comes to about even, overall. Also, he exercises regularly when not in a rush to save the world, and all that magic probably burns extra calories.
A rather horrifying version includes the entire Taxxon species from Animorphs, who have a maddening hunger that makes them eat anything they can — including any injured member of their species or, on at least one occasion, oneself. This hunger is so powerful that when Taxxons are caught up in it (which is a lot) even the Yeerk inside can no longer control it. To its terror. There's a reason that only lower-ranking Yeerks are assigned to Taxxons.
Ax, in human morph.
Klößchen (Grunter in the English version) of TKKG is one. His German name means "Dumpling".
Harry Potter: Ron Weasley. It's a Running Gag to have him cheerfully stuffing 'self out at the feast at the beginning of every year at Hogwarts, sometimes grossing Hermione and Harry out. In Deathly Hallows, it gets even worse. Because, you know, they're out in the wild, without any food, and anyone who fits this trope is going to seriously chow down when the opportunity arises. In the "years later"-epilogue, he has grown a fair bit around the waist.
In The Shattered World, a thief who'd taken professional pride in his slender physique is cursed to be a Big Eater by a sorcerer he'd attempted to cheat. He downs a huge ale and a platterful of meat before being thrown out of the bar puking, already feeling his perpetual hunger's return.
The classic example of this in literature would be Falstaff in Henry IV, who was always drinking, eating, or sleeping. He also was the namesake for the term falstaffian which is now used to describe these people.
Fermín from The Shadow of the Wind blames his thin build on his incredible metabolism, which he displays throughout the book.
Mulch, in the Artemis Fowl series. Let's not get into what he eats, please.
Lieutenant Hélène Froissy, in Fred Vargas's thriller novels. She is seen eating a lot, and hides food wherever she can, including in the police station; the other policemen know this and use her food reserves as emergency supplies.
Graystripe from the Warrior Cats series is called this by other characters, though we don't actually see him eating large amounts.
Tigerstar possibly pushed him into it, forcing him to eat extra mice he would feed to Yellowfang in Firestar's place in Into The Wild.
Luke in Eight Days of Luke, which makes sense considering that he's really Loki, who once almost won an eating contest with the anthropomorphic personification of fire. Also, by the time the book opens he's been imprisoned for quite a while.
Joel Duffle in Damon Runyan's short story "A Piece of Pie", a competitive eater who consumes a huge amount of food during the story, but "does not look as if he can eat his way out of a tea shoppe".
Katniss Everdeen of The Hunger Games eats like a starved wolverine when given the opportunity. Justified in that she comes from the poorest district of an oppressive regime, where starvation is a constant threat, and thus food is often on her mind. Her leanness is explained by her inconsistent access to food, and how much energy she expends to provide for herself and her family.
Subverted by most of the Capitol. They can afford it, of course, but most of them still only have so much room in their stomachs (it's also stated that Capitol citizens consider thinness attractive). This doesn't stop members of this decadent society from gorging themselves, however; at feasts, enormous portions of food are served with the expectation that guests will induce vomiting multiple times over the course of the meal. Naturally, Katniss and Peeta are disgusted when they learn of this at the end of their Victory Tour.
In the first Galaxy of Fear book, twelve-year-old Zak Arranda tackles a free meal with such enthusiasm that only the Wookiee keeps up with him. ...though it probably helps that everyone else at the table was talking, and necessarily eating more slowly.
Day from Best Served Cold eats constantly. Her mentor scolds her for munching buns while they are waiting for assassination targets.
Sigfried Smith from Rachel Griffin consistently takes huge portions of food, as he's used to being starved by adults and wants to stock up while he can.
Mat becomes one briefly in the third book of The Wheel of Time as the result of extremely taxing magical healing to remove a Hate Plague. He has to eat the equivalent of fifteen big meals a day or he'll starve to death. When his appetite returns to normal later in the book, he continues to waste huge amounts of food to annoy his host, but regrets that when he reaches a city that is rife with famine.
The main character from Starship Troopers, though it's justified by the extreme levels of physical conditioning they are put through. The main character at one point mentions eating a breakfast consisting of six eggs, fried potatoes, ham, hotcakes and toast, and immediately thereafter hitting the town to find a proper meal.
In the Rainbow Magic series, all of the goblins love food and are very greedy about it.
The Orange Duke in Gianni Rodari's The Adventures of Cipollino.
Most senior wizards spend their days eating huge meals. Most (but not all) of them are overweight as a result. Exceptions include the Bursar (who mostly lives on his nerves) and Rincewind. Their Hogswatch dinner has something like twenty courses, and is considered something like an Olympic sport.
It actually seem that a Wizard's competency and power is directly proportional to how much he eats and how big he is. As seem with the Dean on Reaper Man (who is easily the fattest wizard of the book, but has the power to cast three ludicrously powerful spells at the same time with a delay, to explode/implode a parasitic supermarket) and Rincewind in general.
Although actually an object, one of the defining traits of the Luggage is that it seemingly eats everything and anything that stands in its way. Just don't ask where all that ends up at, as the characters themselves, who occasionally go to the Dungeon Dimensions (a very bad place), are terrified of wondering.
Whether the Luggage fits depends on your definition of eat, since it doesn't do it as a regular life-sustaining action, and when it does do it, what, if anything it gains from it is questionable.
Keldas of Nac Mac Feegle clans in general, such as Fiona, as seen in the Tiffany Aching books. When she's sharing a meal with Tiffany, she takes only slightly less than what Tiffany has — and while Tiffany is a 15-year-old human girl, Fiona is 6 inches tall. Justified as she is pregnant all of the time.
Restauranteur All Jolson combines Ankh-Morpork's finest examples of Big Eater and Supreme Chef in one person, which the city considers a match made in mashed potato heaven.
Mary Gentle's recurring character Baltazar Casaubon seems to always have a snack at hand. And yes, he's fat... but, to paraphrase Gentle herself, it's more accurate to say that he's a huge guy who happens to be fat.
Lula from the Stephanie Plum books is a very fat bounty hunter's sidekick, and is seen eating about half the time she's in the scene. Stephanie herself is one in regards to cake, but is only of average weight. Other big eaters in the series are Stephanie's sister Valerie (during pregnancy) and Bob, the Big Friendly Dog Stephanie and on-again-off-again boyfriend Morelli share.
Caramon Majere during the Dragonlance Legends series, although he eventually gets back into shape.
Oblomov himself and also Tarantyev's buddy Ivan Mukhoyarov (brother of Agafya), who likes to spend his money on delicacies instead of more visible luxuries (if only because people could get suspicious - as he says, they can't see what he has in his stomach).
Bruce Bogtrotter in Matilda swipes a slice of cake from The Trunchbull's stash. By way of punishment, she makes him eat a cake. (He manages, although he's completely zonked in a food coma at the end.)
Seems to be a rather common trait in Roald Dahl's stories. Most are less sympathetic than Bruce- there's the famous Augustus Gloop, who eats tons of chocolate bars and Bruno Jenkins of The Witches, who is easily lured by the titular antagonists with the promise of chocolate and later becomes a very gluttonous mouse.
Winnie-the-Pooh. At the beginning of the first book he cleans out Rabbit's pantry. In the second book he eats Tigger's lunch and Roo's. And he's incapable of carrying a pot of honey from A to B without devouring its contents along the way!
Nicely-Nicely Johnson and Violette Shumberger in Damon Runyan's short story "A Piece of Pie". She participates in an eating contest and he is her coach, despite being on a strict diet himself. At the end of the story, he leaves the fiancee who has put him on the diet and runs away with Violette.
Nathaniel "Ned" Robbins in Jelly Belly starts out as this. His friends at summer diet camp are straight examples, especially Richard. And Richard's parents.
In Harry Turtledove's Tale of Crispos the healer-priest sent to deal with the cholera outbreak explains that although monks are supposed to be frugal eaters, healers are an exception.
In Mercedes Lackey's Valdemar universe, Heralds, Healers, and Mages who over-use their powers have to be force-fed sometimes.
Baloun from The Good Soldier Švejk loves to eat, and almost always feels hungry. Since he serves in the Austro-Hungarian army in World War I, this trait gets him into a lot of trouble.
"A centaur has a man-stomach and a horse-stomach. And of course both want breakfast. So first of all he has porridge and pavenders and kidneys and bacon and omlette and cold ham and toast and marmalade and coffee and beer. And after that he tends to the horse part of himself by grazing for an hour or so and finishing up with a hot mash, some oats, and a bag of sugar. That's why it's such a serious thing to ask a centaur to stay for the weeekend. A very serious thing indeed."
Mahaut d'Artois in The Accursed Kings isn't exctly fat, but she is described as a big, large, strong woman with a ferocious appetite, to balance her nephew Robert d'Artois. In both the TV versions, she was played by relatively frail actresses, probably in order to make them opposites rather than reflexions of each other.