The Luggage will eat, quite literally, anything that gets in its way. This includes people (on many occasions), sharks, legendary grimoires, and even (on one occasion) a demon. This is combined with its Hyperspace Arsenal capacity to ensure that regardless of what it eats, the next time you open it all you find is your clean laundry. According to Rincewind (its owner) at one point, the only time it ever disliked what it ate was a book of spells — it sulked for three days and then spat it out.
The Tsimo wrestlers (parodies of Sumo wrestlers) of the Counterweight Continent also seem to fit. One man was rejected as a Tsimo wrestler when the trainers gave him a meal and he didn't eat the table, too.
Scalbies are briefly mentioned in Pyramids as a scavenging seabird that would eat things that would make a vulture sick. (And indeed, things that had made a vulture sick.)
In Discworld//Unseen Academicals there's a mention that one of Glendas neighbours apparently regularly drinks paint.
One of the "Utopias" in John T. Sladek's satirical short story "Heavens Below: Thirteen Utopias" depicts a family enjoying a picnic at a landfill site, eating the garbage as if it were the most delicious snack food anyone ever tasted.
In the Perry Rhodan setting, the inhabitants of the planet Halut — four-armed and only somewhat loosely humanoid giants routinely growing taller than ten feet — are capable of chewing and digesting virtually anything, including rock.
As seen in the quote above, the Andalites in Animorphs fit this trope whenever they morph into something with taste buds.
The Taxxons are, as a race, plagued by insanity-inducing hunger. If one sees something that looks like it might be edible and isn't likely to kill him eating it — even if it's his own entrails after being shot in half, or a similarly-wounded buddy — CHOW TIME! They absolutely hate this aspect of their species, and the major reason they surrendered peacefully to the Yeerks was the hope that the Yeerks' mind control abilities would be able to overpower the Horror Hunger (answer: nope).
The Rirhait, a vaguely centipede-esque alien species from the Young Wizards series, are this in a big way. One important point while introducing a Rirhait to human cuisine is to stress that the plate, silverware, table, and floorboards are not to be considered part of the meal.
When a Rirhait construction crew repairs a wrecked building, they eat the rubble instead of throwing it into a dumpster.
In one of Keith Laumer's Retief stories, a race of hostile aliens called the Basurans can survive on a diet of raw metals and silicon if necessary, and, having consumed most of their own planet, are looking for new planets to eat. They were bribed into cancelling an invasion by shipping them another planet's garbage as "gourmet food".
In Robert A. Heinlein's The Star Beast, the title creature (nicknamed "Lummox") could eat just about anything, including concrete, steel, wood, rose bushes, hay and dogs (among other things).
Mulch Diggums, a dwarf from the Artemis Fowl books by Eoin Colfer, has a one-way digestive system and travels underground by eating through dirt, rock, etc. and expelling it behind him. That is one thing all dwarves can do slower or faster. Anything found in earth, like beetles, is food for dwarves as well. A large chunk of granite managed to temporarily constipate Mulch, though. Other features of dwarven biology in Colfer's books include, for example, slightly fluorescent saliva that hardens in contact with air, a detachable lower jaw, and the ability to weaponize the built-up air from consuming soil.
Ungoliant in J. R. R. Tolkien's The Silmarillion seems to exist solely to devour. Her insatiable hunger even seems to scare the crap out of the other main villain, who is a freaking demigod!
Bored of the Rings introduces the Boggies, "an unattractive yet annoying people...slow and sullen, and yet dull", some of whom, on receiving invitations from Dildo Bugger to his birthday party, were so filled with ravenous greedy anticipation that they ate the invitations on the spot.
Miranda Silver in Helen Oyeyemi's White Is For Witching is a pica sufferer who habitually feeds on chalk and plastic. She's deathly thin because of her general avoidance of actual food.
The creature in The Clone. Humans and animals are absorbed and converted, as are certain types of fabrics, but it also likes rubber and concrete — car tires, shoe soles and parts of buildings. When it comes to clothing, the "clone" is a picky eater, though; it'll eagerly convert nylon but cotton is rejected and left behind for some reason. It even resorts to cannibalizing itself when its food supply starts to dwindle, which ends up killing it.
All demons in The Riftwar Cycle — technically they feed on the life energy of their victims (whether mortals or other demons), but they do this mostly by just shoving whatever they want to feed on down their gullet. Because of the true nature of their feeding, though, they can take on qualities of what they eat, and this is in fact how demons rise in power. Maarg, a demon lord and The Caligula even by demon standards, gave full range to his appetites and was grotesquely obese, but also was practically a Physical God in power thanks to his gluttony.
Downplayed with the Horneaters of The Stormlight Archive who, as their name suggests, eat the horns, shells, and bones of their food. It's rumored that they also eat rocks, and one notable Horneater served up chull dung as gourmet food.
A few examples from The Bible of eating food that is unusual or outright forbidden:
The diet of John the Baptist consisted primarily of locusts and wild honey, which, considering that he lived in the desert, was probably all that he could get his hands on. (Matthew 3)
A metaphorical example — Peter had a vision of being presented with all sorts of animals that were considered "unclean" by Jewish law, which God told him to kill and eat. This was an indication that he was to start spreading the Gospel to the Gentiles. (Acts 10)
Paul writes that it's perfectly OK to eat food that has been sacrificed to idols, another big no-no under Jewish law, with the caveat that it shouldn't be done in front of someone for whom it would cause a problem. This is part of his general theme that Christians are no longer bound by rules but by conscience. (1 Corinthians 8)
In the book of Revelation, John is given a scroll and instructed to eat it. He does so.
Ralph Waldo Emerson's poem "Mithridates," about the ancient King of Pontus who was famed for eating small doses of poisons to gradually build up an immunity to them. Emerson turns the poison-eating Up to Eleven by having Mithridates claim literally everything in the world, edible or not, for his food.
Mark Twain (repeatedly) claims that the camel eats anything.
The Commonweal Entelechs can eat ANYTHING, from rocks, to abstract concepts, to entire species.