Assassination Classroom: Although he prefers sweets and other actual food, Koro-sensei seems to be able to eat just about anything, including coconut shells, metal, explosives, paper, and poison.
Bleach: Nel is capable of eating anything. The databooks mention that when she's hungry she looks at her servants in an odd way that make them fear she's going to eat them. One of her trademark powers, which no other arrancar shares, is her ability to eat ceros, combine the eaten cero with her own power and regurgitate back at her enemy at double the power it originally was. Her Animal Motif is the goat-antelope and she has the Extreme Omni-Goat jokes to go with it.
Hororo on Bottle Fairy is usually a Big Eater, but her constant sleepiness and the fact that everything reminds her of food sometimes leads her to unconsciously try to eat the first thing in front of her, whatever it may be.
Ga-chan, the weird flying space baby from Dr. Slump, has been known to eat cars and other inanimate objects. The only thing she - or they - won't eat is rubber.
In the aptly named anime and manga Eat-Man, the hero Bolt Crank could consume just about any tool (usually a gun of some kind) and later reproduce it out of his arm, intact even if he ate it in pieces.
All Dragon Slayers in Fairy Tail have this as an ability. However, they're best at eating their natural element (Natsu eats fire, Gajeel eats metal, etc.), and anything else will mostly likely leave them sick afterwards (though if they're lucky, they'll get one hell of a power boost before that happens). This leads to some What Kind of Lame Power Is Heart, Anyway? when we meet the Sky Dragon Slayer...who eats air.note Though, when you factor in the fact that the Dragon Slayers need to eat their elements to stay at full power (Natsu was once nearly defeated because he couldn't find any fire to eat), and remember just how abundant air is...
Gluttony can (and will) eat anything. Anything. Live people and scenery included. Having acid for saliva certainly helps.
When Edward, Ling, and Envy are trapped inside Gluttony, Ed seems pretty comfortable with eating boots to survive (probably as a result of his foraging on the island Izumi left him and Al on). Ling eats one too, though he's less pleased about it.
Guu from Haré+Guu is capable of eating anything, up to elephants, whales, and people with a single bite. In one occasion she even ate such metaphysical things as another person's dream of herself. She is fully capable of spitting out anything she's eaten completely unharmed, making the effect comically disturbing rather than disturbingly sinister.
Crunch in Mighty Orbots is an extreme omnivore robot by design, as his main function is the team's power source. He can convert anything he eats into energy to use in the team's united form.
Villain Wapol has the powers of the Munch-Munch Fruit, which gives him the power to eat anything and duplicate its effects. For example, he can swallow a cannon and fire it at will, and at one point he eats his flunkies Chess and Kuromarimo, then combines them into a four-armed super-flunky, Chessmarimo (though as Sanji points out, they're just wearing one costume while one stands on the other's shoulders). Wapol even manages to eat himself in order to slim down enough to fit through a narrow door.
Luffy swallowed a plate whole during the celebration at the end of the Arlong Arc. He later ate the bones of a giant fish at Reverse Mountain, and much later on at Thriller Bark ate the bars of the cage holding him.
Near the end of the Fishman Island arc, Zoro and Sanji get into another spat, with Sanji threatening to put knives and other sharp things in Zoro's food. When Zoro is next seen eating, he's making loud crunching noises, and an SBS confirmed that yes, Sanji made good on his threats.
There's not much attention drawn to it, but Cavendish spends a lot of his screen time eating. In a proper, dainty manner. At one point, he starts plucking the petals from the rose he was carrying around and eating them before finally stuffing the whole thing in his mouth. A borderline example, since you can technically eat rose petals raw, but...
Gible is able to eat things like rocks, bicycles (though he leaves the rubber intact), and an entire Team Rocket mecha.
To a lesser extent is Jessie of Team Rocket, who can stomach the horrible cooking skills of Misty and May where others (humans or Pokémon) cannot, and even enjoys them.
Snorlax will attempt to eat anything that moves or doesn't. If it's mouth-sized, it's going in.
More of Extreme Omni-drinkers, but hey. From The Prince of Tennis, Shuusuke Fuji and Kei Tanishi are able to drink down Gargle Blaster-type concoctions that usually knock ANYONE else but them out. The only exception would be Inui's Aozu, which knocked the lights outta Fuji once.
One of the Ranma ˝ OAV series has the minor character Kurumi, a Big Eater who can wolf down an entire feast prepared by Akane Tendo, the resident Lethal Chef (with minors in Cordon Bleugh Chef), and not only consider it delicious, but actually ask for more.
Plue, the mascot of Rave Master. His diet consists almost entirely of suckers, but it used to be based around beetles. He's also eaten a sign and a porcelain doll.
Gourry Gabriev from Slayers is sometimes shown as an Extreme Omnivore. For example, when a crooked cook serves fake, unpalatable Dragon Cuisine to the party, he is the only one who does not feel anything wrong. But subverted in the first season, when he refuses to eat fish guts.
Similarly, the title character of A Certain Magical Index can eat any food. In the very first season, she ate decomposing salad and complimented Touma for the "revitalizing" sour taste. Touma, who was purposely trying to scare her away with inedible food, was thoroughly squicked out by it.
In the manga Toto (not to be confused with its successor Toto! The Wonderful Adventure) by Yuuko Osada, Toto is a dog/dragon that becomes the main hero's left arm. Its power? Devouring anything and reproducing it. Eating a squad's worth of machine gun and becoming a 10-barrel version of all those machine guns combined? Check. Eating a panzer armor to become a big slab of steel shield? Check. Eating an entire theme park to use anything from go-karts to roller coasters as a weapon? Check too. And oh, it once ate a BFS; carnage ensues.
Eriko Futami from Kimi Kiss has been called taste blind due to her eating stuff like Berry Ramen and putting honey and mayonnaise on chips.
Yue from Negima! drinks weird beverages such as salt water.
While some of the cast of Dragon Ball are prime examples of Big Eaters, some of them would also fall under this heading.
In his youth, Goku was very naive about the outside world and thought with his stomach a lot, which more than once lead to him believing a person, thing or concept he'd never heard of before was something to eat.
In his first appearance, Yajirobe kills, cooks, and eats one of Piccolo Daimao's monstrous dinosaur/demon-like henchmen. Even Goku thought that was weird.
Syn Shenron from Dragon Ball GT consumes the seven Dragon Balls to gain the power of the previously defeated Shadow Dragons, becoming Omega Shenron. Later when Syn attempts to do so again, Goku decides to eat the Four Star Ball (his grandfather's keepsake) to prevent Omega from reaching full power and to keep Nouva Shenron from being corrupted. While Goku's attempt is more painful, he was successful in what he planned.
Vegeta's first appearance has him eating an insectoid soldier he had presumably killed earlier. It would seem that extreme omnivory is a Saiyan trait.
The titular character graduates to this in the "Gourmet Casino" arc. With the help of Komatsu's cooking skills and Coco's Batman Gambit, Toriko is able to eat explosive and poisonous ingredients. When Livebearer taunts him for eating the equivalent of dynamite, Toriko retorts that there is no such thing as a "miss" ingredient — to him, all ingredients are blessings.
When the Gourmetcorp attack the Cooking Festival, Grinpatch effortlessly sucks up Coco's poison- and asks for seconds.
Eating Acacia's fish dish ANOTHER allows you to become this. It's actually required to become this since other parts of his full course can't be eaten otherwise.
Demon King Neo may be the most extreme example in the series and possibly all fiction, surpassing even Matter Eater Lad. One of its main methods of fighting is to eat the energy of its opponents' attacks. It even eats a supernova.
Demon King Neo may have a rival in the fully mature GOD. In its debut it eats the Moon.
Dead Master in Black★Rock Shooter: Innocent Soul doesn't just eat souls, she also while sleeping in the same bed as Rock, ate a teddy bear and half of Rock's pig tail.
Mehitak, one of the five Nodos in Heroic Age may avert the letter of this trope, but embodies the spirit of it to a degree only surpassed by Matter Eater Lad himself. Specifically, his Tribe, the Poros, don't eat anything living - which includes fruits and vegetables. Instead, they can - and will - eat any dead matter. Including metal. At one point, he eats a plate of bulletproof superalloy from a pile of Humongous Mecha spare parts and comments that it is 'a bit bitter'. He still decided to have another one, though, much to the consternation of the Humongous Mecha's OWNER.
Though most of the time she's eating carrots, Ryo-Ohki of Tenchi Muyo! is this as she's shown taking a bite of Mihoshi's gun when she finally confronts the "dreaded criminal".
When the characters from Axis Powers Hetalia are discussing what they would do if aliens invaded, England pointed out that they would have a lot of dead aliens laying around afterwards, which prompted China to exclaim, "Leave the cooking to me!". Kinda justified since China is a Supreme Chef in canon and one of the National Stereotypes about Chinese people is that they'll eat anything.
Suu the Slime Girl in Daily Life with Monster Girl is immune to being poisoned and can eat anything that's organic. She's the only member of the cast who can safely eat Miia's cooking. She told Kimihito that she'd be happy to just survive on a diet of garbage in order to make his life easier by reducing how members of his Unwanted Harem he has to feed, but he said that since she's part of the family she should eat with everyone else.