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The Tyranids from Warhammer 40,000 are the ultimate Omnivores, eating everything up to and including entire planets right down to the bedrock, including the atmosphere.
Orks get a special mention for the sheer robustness of their physiology. For example, one "sport" Orks engage in is a face-eating contest, where an Ork and a face-eater Squig try to see who can eat the other's head first. Also, Ork Fighta-Bommas include fuel lines routed through the cockpit, in case the pilot gets thirsty.
Space Marines are capable of eating pretty much anything, since their Bio-Augmentation gave them a 'pre-stomach' organ called the Preomnor which neutralizes anything indigestible or poisonous to them before it enters the stomach. This can also be tactically beneficial, as other organs allow their taste to be strong enough to notice specific chemicals, allow them to potentially track targets by tasting an area. Their bones are also extremely strong, because yet another organ allows them to digest ceramic-based chemicals put into their diet to toughen them.
The Ogres from Warhammer Fantasy are an entire race of Extreme Omnivore. Their whole society revolves around eating, their magic is practiced by Butchers who devour meat, rocks, or other objects to cast spells, and their god is called The Great Maw. A section in their army book involves someone autopsying one and finding fourteen kilograms of raw meat, a whole horse skeleton, rocks, bones, clothes, a sword, and a pistol, which was the cause of death (it went off when the Ogre swallowed the arm holding it, and shot into the base of the Ogre's brain). Gnoblars (small goblin-like creatures) are virtually the only thing they don't think are good for eating — they use them as pets, servants, and cannon fodder (sometimes literally).
In Dungeons & Dragons 3rd edition, there was a prestige class called the "Flux Adept" which, among other abilities, allowed you to derive sustenance from any substance. Gold, poison, dust, anything.
Also, dragons are stated to be able to eat and digest just about anything, including dirt and rocks.
D&D dragons can eat any thing but prefer anything that can be affected by their breath weapon (makes it easier to digest). They have preferences, of course; red dragons (the most powerful evil dragons) are the ones who are most notorious for being man-eaters and desiring the flesh of human and elven maidens.
In 4th Edition, and maybe others, dragons can use the magic of some items they sallow.
What about the Tarrasque? Once every few years/centuries, it wakes up and goes on a spree of destruction, eating EVERYTHING in its path- including entire towns, buildings and all.
In the Planescape campaign setting, there is a Sensate Alchemist that personally samples all of his potions and never refuses an offer to try something new, however hazardous it may be.
In the 3E Ravenloft supplement Van Richten's Guide To The Walking Dead, the Weathermay-Foxgrove twins take on an undead Extreme Omnivore: the Glutton of G'henna. This ravenous ghoul-like creature broke into houses or barns and ate every scrap of food there, whole livestock included; it could be tracked cross-country by the large bite marks it left behind in trees and boulders. It did eat people, or parts thereof, if they got between it and food, but was not a man-eater by preference.
In Nomine, a game about war between Heaven and Hell, includes Haagenti, the Demon Prince of Gluttony. Not only does Haagenti eat pretty much anything, his servants can get an attunement to eat anything they can bite through. According to the game's entry about Haagenti:
"The world is starving - it must be fed. Just don't stand too close, or you might lose an arm. (Mmmm. Arm.)"
Prometheans are also capable of eating practically anything organic — mounds of dead leaves are specifically cited as perfectly valid sustenance. Developing an extra gallbladder or the Acid Stomach Merit expands this to include anything that the character can swallow, though the book does point out that it only reduces the obvious consequences of consuming such things as shards of broken glass, and does not increase the Promethean's jaw strength for chewing the matter in question. Gulping down small pellets of, say, titanium would work; trying to eat one's way out of a thick-barred iron cage is another question entirely.
The Unfleshed, Ridiculously Human Robot Prometheans, can even eat such things as rubber tires and drink motor oil by default... but this actually hurts their Karma Meter. The reason? The Promethean Karma Meter is Humanity, which represents how well they mimic humans, and human beings, as a rule, don't eat rubber tires - doing something like this is a blatant reminder that you aren't a human being, which damages the illusion.
The cosmic level of Universal Digestion in GURPS allows the character to get sustenance from anything with the sole exception of antimatter. Surviving what you eat, is a different matter entirely but easily covered by a couple of other Advantages.
In Paranoia, Matter Eater mutants can eat anything (including evidence of their treason), while those with Toxic Metabolism can eat poison and exude it through their skin. (This being Paranoia, sometimes these powers don't work right. Ow.)
The Epic Stamina knack "Inner Furnace" from Scion grants you the ability to eat any organic object without penalty and drink any quality of water. Its upgraded version, "Devourer", takes away the "organic" and "water" requirements - now you can subsist on anything.
RuneQuesttrolls definitely fit this trope. They're cannibalistic (and will eat other intelligent species), and they can eat things like leather boots, wax candles, and even rocks for food.
Champions adventure "Bad Medicine for Dr. Drugs''. The teen superhero "The Masked Avenger" had the ability to bite through and eat just about anything, including non-living material and plants. It didn't say whether he could use it to eat living animal flesh.
Shadowrun. The Awakened creature called the Juggernaut could eat plants, animals, rocks, scrap metal, etc.
Grim Stalkers from New Horizon are perfectly happy chowing down on humans OR (or rather, AND) Wafans. And can digest and use the materials from both. They also happen to be the planet's top predator.
The card description of the "Enormous Baloth" in Magic The Gathering lists the creature's diet as consisting of "...fruits, plants, small woodland animals, large woodland animals, woodlands, fruit groves, fruit farmers, and small cities."
In Rocket Age Iotes, a race used to living on a post-apocalyptic cesspool of a moon have to be this. They're utterly immune to poisons as a result and can gain nourishment from a bin full of wood-chips.