Endless Space has an entire civilization of these called the Cravers. They are capable of digesting any form of plant or animal matter. Oh yeah, they also consumed their entire home world and are now doing the same thing to other planets.
Also Kog'maw, the "Mouth of the Abyss" whose entire skillset, including his auto-attacks, involves spitting digestive fluids at his enemies. The only reason he's even in the League is because he was told it had the finest food Runeterra had to offer. Ironically, he's never actually seen eating anything.
Kog'maw's Background:The enchanting colors and aromas of Runeterra intoxicated Kog'Maw, and he explored the fruits of the strange world the only way he knew how: by devouring them. At first he sampled only the wild flora and fauna he happened across. As he traversed the parched Tempest Flats, however, he came upon a tribe of nomads. Seemingly unhampered by conventional rules of physics, Kog'Maw consumed every nomad and any obstacles they put in his way, amounting to many times his own mass and volume.
Seems to come with the territory for those who actually hail from the Void. Kha'Zix's goal in life is to consume the most dangerous creatures in the land (Rengar being on the top of the list) to become the perfect predator. Much like Kog'maw his abilities don't reflect the "consume" part of this, instead focusing on his ability to adapt and evolve.
Mass Effect: The krogan come from a Death World where until the invention of gunpowder the #1 cause of death was still "eaten by predators." (Afterward it was "shot to death by another krogan".) Their versions of dogs, varren, are just as nasty. Opportunistic omnivores, they are both scavengers and pack hunters, but they prefer live meat. They are so nasty that feral varren have caused mass extinctions on almost every world they've been introduced to. It doesn't help that they apparently breed like rabbits, can survive in almost any environment, or that they're so aggressive that the Alliance recommends using a squad of heavily armed Space Marines to hunt them.
The krogan themselves are suggested to be able to eat just about anything even vaguely edible, to the point that Grunt (the krogan teammate from Mass Effect 2) finds burning, plague-infected bodies appetizing. However, he draws the line at ramen.
Naked Snake/Big Boss from Metal Gear Solid 3, whose conversations with his medical contact mostly revolved around how tasty the latest animal he'd captured or killed was. Among the items on his menu were various poisonous snakes, ("Cannibal.") mushrooms, crocodiles, frogs, tropical birds, rodents, and ramen noodles.
He is such a glutton he repeatedly asks how delicious a Poison Arrow Frog and Fly Algaric are, in spite of the fact of being repeatedly told that both are instantly lethal to consume.
Monster Hunter Tri has Deviljho, a dangerous endgame-level monster only encountered in the online mode. It's an Extreme Omnivore not in the "eats cars and lightbulbs" sense so much as apparently having no standards for what kind of meat it'll eat. On top of being a voracious predator that hunts nonstop due to its extremely high metabolism (to the point of driving other species to extinction, according to the game's description), it's also been observed in actual gameplay to munch on slain or captured members of its own species as well as its own severed tail.
In Persona 4, the main character Yu Narukami can check the refrigerator on certain days and eat things that he finds within to increase his courage. These include such delicacies as expired milk, white miso (which used to be red), and his cousin's science experiment, which is a pot of grass. This has become a bit of a joke in the Persona 4 fandom.
Flynn Scifo in Tales of Vesperia will eat nearly anything, resulting in him becoming a Cordon Bleugh Chef. Making things worse, his reaction to people disliking his cooking is to come up with even worse combinations to "improve" the flavor.
Pit from Kid Icarus: Uprising is said to be this. He himself even mentions eating ice cream off the floor!
Yoshi, first appearing in Super Mario World, can eat almost anything that moves with his long sticky tongue. Adding to the fun, in later games, things he eat get crapped out as eggs (apparently empty ones). Yoshi's stomach has gradually grown less sensitive in each game he has starred in. In Yoshis Story, the newborn Yoshis (except for the hidden black and white ones) would prefer specific foods over others, even take damage from eating things they didn't like, like black Shy Guys or hot peppers. In Yoshis Island, his tongue would bounce off of spiny, large, or tough enemies. In Super Mario World, he could eat pretty much anything.
In Paper Mario: The Thousand-Year Door, the three dragons, while intending to eat anyone they see, also eat the treasure you get for defeating them. Before Mario fights each of them, Hooktail ate the Diamond Star (which Koopley found inside her), Gloomtail ate a treasure chest containing the Star Key (coughed it up after he was defeated), and Bonetail ate a chest containing a badge (also coughed it up once defeated) and he's not even alive.
Dimitri in The Legend of Zelda Oracle games will eat any enemies Link comes across while being ridden. Funnily enough, in both games he is nearly eaten before Link intereferes, in Seasons by some Moblins and in Ages by some Tokay. The Tokay themselves gladly ask for some Ember Seeds to eat in place of Dimitri, though they don't actually end up liking them so much.
The Pikmin's Onions may also be an example, they consume pellets and the remains of defeated enemies (including things like pearls) that the Pikmin bring back to make more Pikmin. Kind of like a real-life ant queens.
Wario can eat pretty much anything in Super Smash Bros. Brawl with his Chomp move (Poke Balls being one of the only items he can't eat), making him similiar to the better known omnivores that appear in the game. This includes his motorcycle. In Smash Bros for the 3DS/Wii U, it's been upgraded further, as he can now eat virtually any projectile, on top of regaining health and building gas for the Wario Waft when eating items.
And "Cook" is just an upgraded version of "Eat" her(?) normal skill that does the same thing.
Knights of the Old Republic has the cannok, kill them to retrieve the stuff they ate. Their flexible eyestalks are good sushi too, so the main character counts also.
Online game example: Skeiths and Grarrls, two types of virtual pets in Neopets, can eat any inventory item, not just those designated as food.
Izen from Gadget Trial, being a bio-engineered Robot Girl, eats just about anything she can get her hands on. She does have a fondness for dynamite, which, according to her, tastes like bean jelly.
NetHack already allows the player to eat many types of food, but Slash Em Extended takes that up to eleven with the Activistor role. They can eat meat, vegetables, corpses, rock, glass, bone, iron and several kinds of other metals. Plastic is still inedible for them though.
Final Fantasy VIII's Guardian Force, Eden, allows the Junctioned character to equip the "Devour" ability. If used successfully, the character will rush the enemy... and the scene will change to a peaceful, pastoral landscape while horrible chomping noises are heard in the background.
In Jeanne d'Arc, the Team Pet Cuisses can eat almost any combination of two Skill Stones and spit out a new Stone. Most high-level Skill Stones can only be acquired through this method.
Toady from Rogue Galaxy, who Cuisses is an Expy of, can do the same thing with equipment.
Pac-Man. He eats all sorts of fruit yes, but he eats floating dots (and the occasional big floating dot). And blue ghosts. How would you like to eat a ghost? That can't be healthy. Then there's the keys and spaceships.
Fridge Horror sets in when you realize he eats small round floating dots, larger round floating dots...and he himself is an even bigger round floating dot.
Maw, from The Maw, eats a huge variety of creatures, the rocks one of those types of creatures hide under (once he's large enough), an entire planet, and the game's camera. Pretty much the only thing he won't eat are these little one-eyed blobby things.
Darkstalkers gives us Soul Bees. They instinctively attack and devour anything moving object that is not another Soul Bee and rarely suffer from indigestion or food poisoning.
Yoshika Miyako's ability is explicitly to "eat anything and everything". She makes use of it in combat by eating spirits to regenerate health.
The Green Tentacle from Maniac Mansion will eat good food, food gone bad, or anything that just looks like food - in fact, his favorite dish is plastic shaped like food.
Your BOY in Noby Noby Boy can eat anything and anyone. However, he doesn't really digest them, as they come back out in one piece when they're, um, "evacuated".
The Elder Scrolls series has a rather complex alchemy system that uses all kinds of items ranging from normal food, to flowers and fungi, to ectoplasm, zombie flesh, and raw demon hearts. Your character can eat any ingredient raw or brew multiple ingredients into a potion.
This includes inorganic, inedible, or just plain weird materials; such as: ground-up bone, claws, raw silk, teeth, wax, magical salts, horns, scales, demon and human skin, human flesh, troll fat, vampire ash/dust, normal ash, rat poison, various hides, cuttle, soap, pearls, several types of jewels (including diamonds!), metals, glass, rocks, and presumably even more.
Skyrim has a perk which allows you identify all the properties of an ingredient. Would you like some salt on your giants toe and human heart?
Dog in the Fallout: New Vegas add-on, Dead Money. He accidently ate the explosive collar his master, Elijah, gave him in order to keep him loyal. He will also eat the remains of Ghost People you kill, a useful way to make sure they stay dead.
The player can eat, with the right perks, giant insects, mammals,people, boiled toxic cloud, most plant life,super mutants, 200 year old Indestructible Edibles,Ghouls (radioactive zombies), glowing mushrooms and mutant animal guts.
Pep in the Putt-Putt series, especially in Putt-Putt and Pep's Dog on a Stick, where he had more bones than any dog could dream of.
Kingseeker Frampt in Dark Souls serves as your Vendor Trash disposal by eating the equipment and giving you souls in return. He can also break down Titanite material.
Raving Rabbids: a couple of minigames in the first one feature Rayman serving up food to a rabbid by drawing it. Foodstuffs produced in this manner range from the relatively normal (bananas, fish, sausages), to the odd (cans of spam...the can is eaten too) to the absurd (baseballs and cinderblocks.) These are all devoured with every indication of satisfaction.
The skags in Borderlands will eat just about anything, and puke up anything they can't digest (money, ammo, and even the occasional gun) into the "skag piles" you find near their lairs.
In Borderlands 2, Scooter claims that Crazy Earl once ate one of his runners.
Scooter: Yeah, he ate one of my cars once. The whole thing. With a, like, fork.
Dungeons Of Dredmor: The Vampirism skill tree ability "Drinker of the Dead" allows you to eat the corpses of your fallen enemies, whether they be an Animal, Plant, Demon, Robot...you name it.
The Tourism tree has a skill that lets you eat your items, too, with a chance of getting food poisoning which wears off after a few turns.
The monsters in Ether Saga Odyssey eat a wide variety of food, including objects that don't appear to be inedible, such as Oil Pies, enhancement goods, weapons, armor, the list goes on.
In Team Fortress 2, the Heavy has an item called the Sandvich that he can eat to regain health, but he also has a metal version of it called the Robo-Sandvich that he can somehow eat without seriously injuring himself. He can also eat the Festive Sandvich without choking on the gift wrap, lights and ribbons.
The Hungry Pumkin in Pumkin Land, who will happily chow down on bowls of rice, glasses of water and entire salt shakers (including the bowls, glasses and shakers themselves.)
Space Quest VI has a Womb Level inside the body of Roger's latest crush, Stellar. Many of the items needed to solve the puzzles are random inedible items that she has swallowed, and there are others lying around that are just decoration and aren't part of any puzzles. At least the tooth filling and fingernail may have been swallowed accidentally but things like a feather, a staple, a paper clip, a screw, and a coin were definitely swallowed deliberately. This is lampshaded by the narrator, and also by Roger himself later when he lectures Stellar about her eating habits.
The Tazmanian Devil continues his eating habits in Escape From Mars Starring Taz, where all power-ups get eaten by him. Along with food, shrinking potions (bottle and all) and containers of gasoline, there's also damaging power-ups like Cartoon Bombs, bundles of dynamite and cakes with lit dynamite sticking out of them, all of them he'll happy gulp down if he so much as comes in contact with them without spinning into them to destroy them instead. He even eats the exit sign at the end of a level.