Any game that features the Power-Up Food and Hyperactive Metabolism tropes. Finding whole turkeys or cakes inside those oil drums you just kicked? They'll be gone in a second, and you'll always be ready for more.
MakotoNanaya is heavily implied, if not outright stated, to be this. Her introduction in BlazBlue is at Litchi's clinic, having injured herself by falling out of a tree she was climbing for exercise and fun (yeah, she's like that) after eating several platefuls at an all-you-can-eat buffet with her friends Noel and Tsubaki. She's often shown eating snacks and sweets, and one of her winquotes is:
That brings us to Platinum the Trinity, whose intro to the story involves her eating several dish stacks' worth of food like a total glutton - she even does this in Arcade mode, too! Truly, Ragna is cursed - Platinum was the second to dine-and-dash on him, the first being Taokaka.
Possibly even funnier in the original Japanese/DS retranslation, where that "soup" is booze.
Jones in Criminal Case seems borderline obsessed with food, especially things like hot dogs and cookies. Other characters lampshade this with comments such as "do you ever think of anything other than eating?"
Tiki the Fairy from Dragon's Crown is at least implied to be this; though a petite, slender fairy girl who is small enough to fit into a standard sized tavern goblet, she's implied to have single-handedly devoured the enough-for-a-party-of-six spread of food at the player characters' table.
The playable characters are definitely this, if the campfire minigame is any indication: with the possible exception of the stout Dwarf, most of the characters have either slim or muscular builds and can snarf down incredible amounts Sauteed Demon's Heart, Killer Rabbit Stew, and Red Dragon Steaks. The Fighter even proudly declares, "I'm gonna have nineths!"
In Fantasia - Momento of Grand Finale, Nero is a carnivore who eats a lot (mostly inedible). It is even played for laughs most of the time and he claims it to be his magical ability as a half-elf to have an iron stomach.
Sabin from Final Fantasy VI. He isn't even afraid to stop and eat a several course meal of ghost food on the Phantom Train, knowing full well that he is being prematurely taken to the other side.
Prishe from Final Fantasy XI frequently uses food items to boost her stats during battle, and will ask her teammates for food items if she's one of your opponents in the "Heroine's Combat" event. In addition, she has a whole list of secret food-related quotes in the Dissidia: Final Fantasy prequel. Apparently, being a Cute Bruiser burns up calories like whoa.
The Cavalier Lowen, Marcus' right hand in FireEmblem 7. A Justified Trope because he's actually the cook of the party (mentioned in his supports), and he was raised by his father and grandfather, both former cooks for the Pherae royalty.
Syrene: You know I can tell when you're lying. Plus, you not eating is a dead giveaway. I mean, when's the last time you said no to a cookie? It's not a criticism. One of your most charming qualities is how you can outeat anyone. It's because of someone special, isn't it?
There's also the thundermage Ilyana from Fire Emblem Tellius. To start, every support conversation she has involves her being hungry. She joins your party in the 10th game at first to avenge her stomach for being fed scraps that could never satisfy her. However, at her first introduction in the 9th game, the hero assumes she's just ill. Also, other characters accuse her of using her really cute looks to get free food.
Taking this trope to the extreme, Ilyana even complains that she's dying with an empty stomach when she is killed in battle (in a game where non-plot critical characters such as herself die for real). One popular fan theory is that she has a tapeworm. Her character specific ending in Radiant Dawn states that "somewhere, she is hungry."
A possible explanation is that Ilyana might be a Branded from the Laguz tribe. One of the supposed hints is that the Laguz have quite large appetites, just like she does. (The other is that she has uncommonly big Physical Strength growths for a mage, again like the Laguz do).
Ike himself is no slouch in the eating department, having an appetite that's said to rival that of any beast laguz. Especially when it comes to meat.
Stahl in Fire Emblem Awakening is described as "the biggest glutton in the army", and is perpetually hungry. In the "Golden Gaffe" DLC, he tells the first Risen he meets that he was saving gold for a large meal. He says that his dreams is to go Walking the Earth... and taste all the local dishes he can find. (And if he marries Cherche, he is said to have put up weight after eating all her excellent cooking.)
Panne is said to be "the one who wolfs down any food faster in the army" (paraphrased), and the aforementioned Stahl can gain her affections via cooking for her. It's kind of a Justified Trope: she's a member of the Taguel race, and her powers involve shapeshifting into a LARGE fighting bunny with a very physical fighting style.
Nah is said to be one of these too, likely because she's a Half-Human Hybridand a growing teenager on top of that.
Li Xiangfei. Two of her endings show her getting her teammates and friends in trouble for her appetite and several of her winning quotes involve her mentioning food. Her family has a restaurant in South Town, yeah, but oh booooy...
The psychic Sie Kensou is such a big eater that he actually uses eating niku-man dumplings as a special fighting technique that lets him recover health during battles... as long as he doesn't choke on them, that is.
Maxima is this and has a massive Sweet Tooth. A Justified Trope since he must eat sweets constantly due to being a Technopath and a cyborg - glucose is the fuel for the brains, and Maxima's still human brain must handle and process LOTS of data all the time.
In another BioWare one - Zaalbar from Knights of the Old Republic. Mission snarks that he needs "eight squares a day." In his first in-game appearance, he is annoyed with having to back up Mission against a pair of Rodians because "Mission, they just brought my food!" And, when enslaved for maybe a day, became so hungry he bit a hunk out of one of his captor's arms. He is also the party member that approaches you when someone other than him is getting into the emergency rations. Justified in that Zaalbar appears to be the Wookiee equivalent of a BIG teenaged boy.
In a third BioWare game, Mass Effect, the Codex reveals that people with biotic abilities (telekinesis) are big eaters since it takes so much energy to use their powers. In order to stay healthy, they need to eat almost three times as much as a normal person in their position, and they usually take special high energy drinks or bars right after every battle in which they use their power.
Sonia Strumm and Bud Bison, as noted by Geo Stelar, Luna Platz and Zack Temple.
Speaking of Luna, fail to grab her handkerchief in the third game (you have to choose between it, Sonia's fan-gift bag, and Bud's shirt) and watch her gorge on "comfort food". Sonia has the same reaction if you don't pick her hand-bag, and both will pig-out if you save Bud's shirt.
Also Netto/Lan from Mega Man Battle Network. On one occasion in the anime, he gorges on curry until he balloons up cartoonishly, though a couple scenes later he turns back to his usual skinny self.
Bud encounters a little girl named Fay Phamish in 2 who is able to keep up with him in an eating contest. Given that Bud had a four-armed robotic hat stuffing burgers into his mouth throughout that competition, this is more impressive than it sounds.
Naked Snake of Metal Gear Solid 3 would probably qualify for this, as would EVA when you have to escort her. Polishing off two sets of rations (engineered to keep you going for at least a day) in a minute and walking away no less hungry than before? Yeah. The only thing he's interested in during ParaMedic's nature lessons, is whether he can eat the item in question. Add to that the Boss's comment at the beginning of the game about him having lost weight. Suggests his love of food is a little more that just necessary stamina recovery. In Portable Ops, he complains about Sigint's idea to make eating unnecessary for soldiers, because eating is the highlight of his day.
Interestingly done in Metal Slug. Eat too much food and your soldier becomes fat (Uh Oh BIG), which slows them down, but increases the power of their weapons. This trope was the reason as to why Nadia joined the team in Metal Slug 4: so she could lose the weight and go into the modeling business. Also featured in the "Good" ending of Metal Slug 4 as well.
Your average Monster Hunter character can gobble down a comically oversized hunk of meat in about five seconds, and a full meal in roughly the same time. Then there are the armor abilities Speed Eating (Consume meat/healing items faster) and Double Hunger (Lose stamina quickly).
The main character of Persona 3. On one of the dates with Elizabeth, in which the two of them go to all of the strip mall's restaurants, she asks him afterwards if he was alright, as he had "eaten little after our seventh meal". In the Moon social link, the Gourmet King comments on how the main character can eat so much and still stay thin. The main character is also portrayed this way in the manga◊.
The female main character in Persona 3 Portable also qualifies; as Junpei will point out during his Social Links, she orders just as much as he does and has no trouble with it.
Though with Ema, it may more of a Trademark Favorite Food deal - Maya mentions eating quite often, and Ema is only ever seen eating Snackoos. Though she does have a bag of them with her near constantly.
Alex Mercer from Prototype is one hungry Humanitarian, devouring people and other Infected monsters with equal abandon. Instead of becoming visibly fatter, his shapeshifting powers allow him to compress his mass down to normal human size, which is handy given that he's implied to weigh at least a ton.
This obscure children's educational game called "Pumkin Land" ("pumpkin" is intentionally misspelled) featured a mini game that is intended to teach children about different foods. The player plays as a diner worker and has to serve an anthropomorphic pumpkin who eats enough food to feed many people in one sitting. Not only does he eat a massive amount of food but he also eats condiments and cooking ingredients on their own (salt, pepper, jam, and butter) and if he orders a beverage or something that's served in a container, bowel, cup, or shaker; he will eat that with the food!
Batsu Ichimonji and Hinata Wakaba from Rival Schools (though the latter does this only with cake).
Rosita Aries, the Token Mini-Moe in Sakura Wars: So Long My Love. The first thing she does when she joins the New York Combat Revue is demand food, threatening to eat her pet ferret if she doesn't get any soon. She actually has a Freudian Excuse for her obsession with food, since she once was extremely poor.
Hilda's combat abilities in Shadow Hearts 3 actually justify her eating habits — she casts from calories. And if her calories get high enough, she ends up both "curvy" (read: ridiculously round) and barely recognizable.
Xiba from Soul Calibur loves food, with most of his lines revolving around it.
The hidden collectibles for 100% Completion in 'Splosion Man are wedding-sized cakes, which the character proceeds to nom in a single cram (witha slice or two comically bouncing away). Given that he's a being of living fire, he's not going to worry about weight. He also tends to mention various types of meat while doing things. of course, given that slain characters in this game "bleed" meat...
Yoh from Starry☆Sky has a very low tolerance of hunger, and is often vocal about it.
Reid from Tales of Eternia, who states outright several times that he is 'not interested in anything that doesn't fill his stomach', and who is constantly hungry and in search of things to eat. Furthermore, the sole reason he has become proficient in using a sword is so that he can hunt for food in the forests. In the crossover game Tales of the World: Radiant Mythology, there occurs a memorable (and hilarious) scene involving Reid practically molesting Senel (from Tales of Legendia) over a basket of bread that Senel happens to be carrying.
Aside from constantly referencing food in the 8th game, if you take the translations literally, she actually eats a boss during the course of the game, merely complaining of a small bone afterward. Kindasorta justified in that she's a ghost. But only partially. The boss she "ate" made a full recovery in time for the 9th game.
As of Ten Desires, we now have Yoshika Miyako, whose ability is to "eat anything and everything".
Tsukumogami has Saki, a tiny, cute, hyperactive girl who works as the poster-girl at the local We Sell Everything shop - being apparently paid entirely in food, which tends to evaporate around her. However, she's actually a Weasel-spirit in human form, which might explain some of it. Her siblings - talking weasels who lack the spiritual power to change shape - are just as bad, and appear capable of putting away ludicrous amounts of food considering their tiny bodies.
Queen Memory in Twinkle Star Sprites, who is perpetually hungry and (in her ending scene) asks the wish-granting Twinkle Star for an enormous amount of food (plus sherbert for desert). It's suggested her daughter Ran might be the same way.
Cecilia from Wild AR Ms and Lilka from Wild AR Ms 2 are both Big Eaters in the magic user category, although it's only used for a single gag in each game.
Jin from Yo-Jin-Bo isn't shown to eat a lot on screen, but he's the only one to ever complain of being hungry, and when he does, the other guys groan as if that's all he ever talks about.
In Punch-Out!! for the Wii, Piston Hondo is shown eating several times his own weight in sushi as part of his Title Defense training.
An unusual Cool Big Sis example is Deis in Breath of Fire IV. Admittedly, she had the perfectly valid excuse of being imprisoned in a suit of armour named Ershin (that grew to have a mind of its own) for centuries; the first thing she does when she ends up being hosted in the body of a summoner (after complaining about the summoner's figure) is pigging out until she passed out.
This is a gameplay mechanic for the player in Crush, Crumble, and Chomp! Failure to eat regularly makes the monster hungry; if the monster becomes ravenous, the player loses control and the computer takes over.
Alistair from Dragon Age: Origins notes that Wardens tend to become this, especially in the period shortly after their Joining.
Rico in Duel Savior Destiny has an apparently bottomless stomach and is capable of eating a pile of food larger than herself without any ill effect. This makes somewhat more sense when you realize she's barely even a corporeal being let alone human.
Implied with Youtia in Eien no Aselia, who forces Yuuto to make her lunch. He makes enough for at least four people figuring he can serve the rest to everyone else later, but she eats it all before being satisfied. Considering her personality, though, she might not have eaten in days.
Given that the bosses in Evil Twin Cypriens Chronicles are dark reflections of the hero's friends, the fat kid Joey's counterpart Big Joe takes this trope to its extreme: an immobile, enormously fat creature with two mouths who rules over an island mostly made out of food which exists for no other reason than to feed its ruler. The good Joey is imprisoned in Big Joe's stomach.
Big Smoke in Grand Theft Auto: San Andreas not only orders enough food for all four people in the car when the player takes CJ's friends to the drive through on a mission, but he actually manages to eat everyone's meals in the few minutes it takes to finish the car chase immediately after.
Kurumi Kasugaoka, from the sadly cancelled Nintendo DS dating sim Hachikoi. Her character page on the website even allows you to feed her!
Coach is implied to be a big eater in Left 4 Dead 2, but it's never shown since the zombie outbreak kind of ruined his chances of resting so he can eat something big. He likes eating a pizza sub style, possibly having a sweet tooth since he says it's a damn shame the rainstorm in Hard Rain washed all the sugar away, and heavily likes the Burger Tank's BBQ bacon cheese burger with fries, orange soda with no ice, and an apple pie. When the survivors see a wedding in the park during The Parish, Coach may sometimes ask if the others have seen a wedding cake around.
Manpuku in Ōkamiden. He saves Chibiterasu (who he nicknames Pork Chop) from being cooked in a huge pot of soup... by drinking the soup. It's also deconstructed, his compulsive eating means his mother can't afford to feed his dog, so he gave him to a relative. There's rarely any food in his house because he eats it all, and his mother skips meals often.
Misaki Kawana from ONE. This is referenced in the doujin fighter game Eternal Fighter Zero with her "High-Speed Lunch" super.
Hanako from Persona 4, also a Gonk that believes she's gorgeous. When she's on a diet, she eats a bucket of curry.
King Hippo. His intro in the Wii game shows him in a field full of ham and tropical fruit; over three cutaways, he eats everything there.
Bear Hugger of the same series drinks gallon jugs of maple syrup at every meal. He's also fat enough that you can't hurt him by hitting his stomach.
Drang the ogre in Puzzle Quest has five missions where he asks you to procure rare, dangerous monsters for him to eat. One of them, a Wyvern, is requested so that it can kill a Troll he ate that's regenerating in his gut. The fourth one is an ogre, which disgusts your character. When you finish the last mission, Drang joins your party and takes bites out of any Animal-type enemy you face, causing them opening damage.
Gan Isurugi from Rival Schools. Justified as he's built almost like a Sumo fighter and his fighting style is heavily based on Sumo itself.
The de Sainte-Coquille family, who are almost universally large with appetites to match. Max of Rune Factory 2 is still slim, but when Barret makes a cameo in Rune Factory 4, he wonders if Max will one day resemble the rest of his family.
Sonic Unleashed gives us the first time Dr. Eggman has eaten anything on screen. He downs a 12" sub sandwich in two bites, and does it all in under 10 seconds.
The Heavy from Team Fortress 2. He sure does love those sandwviches. He can even earn an achievement for eating 100 Sandviches, which he does with great gusto, one after another. Well, he certainly needs all those carbs to lug around his 150-kilogram minigun, and his belly roll makes for great recoil cushioning.
Barlow of Vanguard Bandits, the ATAC pilot with what he calls a "glandular disorder". He's always eating some candy, and when he gets hungry he starts going after the weirdest things. Ranging from earth-worms to platypi.
The pandaren in World of Warcraft: Mists of Pandaria are an entire race of Big Eaters. In part because of that, most pandaren consider being fat a virtue, and some will even say that your character could stand to gain a few pounds. (Indeed, fat pandaren seem to be barely slowed down by their extra weight.)
Kirby, especially in the Anime Kirby of the Stars, can devour large quantities of food without any consequences — except in one episode where a special snack food makes him (and King Dedede) extremely fat.
Gooey, from Kirby's Dream Land 3 likes to eat just as much as Kirby.
Same with PrinceFluff from Kirby's Epic Yarn. Him and Kirby together managed to eat a mountain sized cake at the end of one of the levels.
King Dedede isn't too much of a slouch on eating either, and has the paunch to prove it, though he sometimes qualifies as a Villainous Glutton, especially when he steals all of the food in Dream Land to gorge his Big Eater habits in the first game. He and Kirby actually compete in an eating contest in Kirby Super Star racing to get the most food.
Storo, the BigGuy of the Squeak Squad is another example of a fat big eater.
Also in HG/SS, School Kid Billy says that Jasmine is a big eater when he tells you that she hangs out at the Olivine Cafe on Wednesdays. If you actually go there on Wednesdays between one PM and two PM, you can find her there, and the rumor is clearly true; she has a LOT of empty plates on her table. (Incidentally, this is how you can get her phone number, something that is needed from a Gym Leader if you want to battle him or her at the Saffron City dojo.)
Munchlax (it's actually known as the Big Eater Pokémon) and its evolution, the most famous Pokémon Big Eater ever, Snorlax, big, fat, always hungry when awake, and capable of devouring whole forests of fruit in less than a day. It will devour its entire body weight in food at least once a month and it weighs over 1,000 pounds.
Downplayed with Larvitar, a Pokémon that eats rocks and stones. According to its Pokedex entry, when preparing to evolve it will eat an entire mountain before turning into the immobile Pupitar.
Another Pokémon family, Gulpin and Swalot, they are living stomachs with expandable mouths that swallow their food whole.
And fifth gen brings us the Deino family. Deino itself is blind and instinctively takes bites out of anything it bumps into (which is everything). It evolves into Zweilous, a Multiple Head Case that fights with itself over food and more often than not ends up eating twice as much. Zweilous eventually gains eyes when it evolves into Hydreigon, an aggressive predator, wild Hydreigon are said to kill and eat anything they see.