Buccha from Air Gear was like this before his Heel–Face Turn. He's a subversion (possibly a double one), though. He's a Big Eater who looks very fat... but he's only got about 6% body fat. He looks the way he does due to blood pooling in his stomach from overeating (which means that his gluttony is the reason he looks that way). When he exerts himself, his ridiculously sculpted body is revealed.
The Titans from Attack on Titan. They exist to eat. They don't even have digestive organs. So when they get full, they puke up the people they devoured, and go eating some more.
King Gurumes from the first Dragon Ball movie qualifies—the Blood Rubies turned him into a monstrous beast with an insatiable appetite which only grows the more he eats.
From the original Dragon Ball anime, both Buyon and Giran fit this trope. Yakon from Z also fits, especially since it ends up in his demise.
His weight is questionable due to his outfit, but Earl Tyrant of Final Fantasy: Unlimited definitely fits the glutton part. 90% of his scenes take place with him eating something or other, usually made from the negative emotions of his "subjects".
Hellsing's Big Badthe Major is the only fat character in the cast, causing a few potshots about his weight from other characters, including one of his own minions, though it doesn't seem to affect him. Additionally, some of the vampires are seen gorging themselves during the series, they simply don't get bigger because of it.
Polpo from Jojos Bizarre Adventure Part 5. Due to his position in the mob, he gets to stay well protected in a posh prison cell, surrounded by food. His Laser-Guided Karma hits him when Giornio changes a gun into a banana and tricks Polpo into shooting himself.
Subverted in Kishin Douji Zenki. One of the first monsters that Chiaki and Zenki face in the anime is one of these, but just like almost every monster in this series he turns out to be an average person under the brainwashing effects of the Karma Seeds; normally he's just a Reasonable Authority Figure who happens to be a Big Eater and the Principal of Chiaki's high school, and when de-brainwashed he returns to his original self without any memories of what happened. The episode even has a short scene where the future victim's large appetite is Played for Laughs and offers a HUGE contrast to his greedy behavior as a monster.
Wapol, who actually has eating as a power: He ate the Baku-Baku (Munch-Munch) Fruit, which not only lets him eat anything, but incorporate the aspects of what he's eaten into his body. In a bizarre subversion though, Wapol ends up being Lean and Mean as well: he actually eats his own excess bulk to fit through a door. Nobody knows how that works. Ask the writer. That'll be good for a laugh.
Commodore Nelson is extremely obese, to the point of immobility, and is almost always seen eating. Alvida, a villainess from an early arc exhibits a distinct cowboy motif and so much pork it's a wonder she can move. She's utterly convinced that she's the most beautiful thing on the seas. Later on she reappears, having eaten the Slip-Slip fruit. In addition to giving her a smooth, frictionless complexion, it seems to have made her excess weight "slip" off as well; she makes a point of stating that "the only change is that my acne is gone", though, so she might not have changed her diet any. (Her name was Alvida the Iron Mace)
Prime Minister Kamiya in Speed Grapher, an incredibly corrupt and greedy high-class politician who is also fat and a Big Eater. It's played even straighter when he becomes an even fatter and uglier Euphoric.
Tokyo Ghoul has several, as a result of the strong focus on food and consumption.
Rize Kamishiro is an unusual example. While she looks like a beautiful and slim woman, she is actually an infamous Ghoul known as "Binge Eater" for her tendency to go on brutal feeding sprees. While normally Ghouls only need to eat a single human about once every month or so, she steals hunting grounds from weaker Ghouls and throws any Ward she enters into chaos with her constant feeding.
Noro, one of the commanders of Aogiri Tree. A towering, silent figure primarily known for his abnormal appetite and an unusual smell of rotting flesh. He uses multiple Combat Tentacles ending in large mouths to devour anything (or anyone) unlucky enough to be within range.
In the sequel, Seidou Takizawa has become one. His transformation into a deranged Half-Human Hybrid is cemented by his enjoyment of going on killing sprees and feasting on former comrades. He's almost always splattered with blood and gore, messily eating his victims in front of their friends.
Midora from Toriko. Ever since he was born he's been cursed with a hunger that cannot be satiated. He is the biggest and most disgusting eater in a series full of big eaters and he founded an entire organization of like-minded individuals. One of the reasons he is searching for the legendary ingredient "GOD" is because it may be the only food that can satisfy him.
Trigun has Legato Bluesummers, The Dragon to the series' main villain, is a much more lean example of this trope, but he's an evil, ruthless sadist who's frequently seen eating, a trait the author wanted to make a humorous quirk for the character, but instead served to make him creepier. Case in point: he even offers a little girl a hot dog at one point...and said hot dog is implicitly made of human flesh...
Beelzebub of is the second youngest of the Stakes of Purgatory. At one point in the side materials, she gives Valentine's Day chocolate to Gohda, the Ushiromiya family chef so that he'll return the favor on White Day (and sure enough, he immediately flies to Belgium). She's even willing to use bits ofher own flesh if she thinks it will make a good meal. She isn't fat, though.
She's regarded as the gourmet of the Seven Stakes, and while she is in fact a Big Eater, she's also notoriously picky about her meals.