Shockeye in "The Two Doctors" spends almost all his time eating, preparing new meals, and thinking about food, although it seems that members of his species can be gluttons without gaining weight.
Grunchlk from Farscape, who always seems to be eating something while on camera — even if it's two of his own fingers.
Boss Hogg from The Dukes of Hazzard was very fat, very hungry (in one show he devours a tableful of chicken wings) and always leering lecherously at Daisy as his white three piece suit strained to cover his bulk. (Not in The Movie, however.) (Sorrell Booke, who portrayed the character, was only slightly overweight. He wore padding under his suit to make himself look obese.)
Ramsay Bolton is in good shape, but he's often seen eating, usually at an inappropriate time or while discussing something horrible he's done in a matter-of-fact way. In Season 5 this is used in a scene that very deftly summarizes him: in the same episode that both Jon Snow and Stannis express their worry about provisions for the long winter ahead (which should finally be coming, in a matter of only weeks)...Ramsay is enjoying a private feast with heaping piles of meat: foodstuffs he should have saved up for the hard times that are coming. Ramsay does whatever he feels like in the moment, without even pausing to think of something as simple as how to sustain his food supply tomorrow.
Walder Frey is much the same. His opening scene in any given episode usually involves him eating in a disgustingly loud fashion while someone is talking to him.
Nerus, a Goa'uld from Stargate SG-1, is a relatively sympathetic villain, for his species. Which means he's a devious but Affably Evil bastard. When he turns out to have become a double-agent for the Ori and remains completely unhelpful to Stargate Command, General Landry figures out how to get his cooperation: no food.
The Pudgy Pig would eat the world's food supply in 48 hours, and even ate the Rangers' weapons. His Kyoryu Sentai Zyuranger counterpart Dora Circe could do likewise, using his Super Speed to snatch people's food off their plates before they could even take a bite.
A less iconic example was the Ravenator, but Rita used a very different strategy with him, shrinking him to the size of an insect and tricking Tommy into swallowing him, which gave Tommy a huge craving for junk food. (When he was discovered, the Rangers deduced that Rita's true plan was likely to use Tommy like a Trojan Horse to infiltrate the Command Center.) In Ninja Sentai Kakuranger, he's the youkai Gakitsuki, and has a very similar power, entering the body of Seikai and giving him an even bigger appetite than ever until he grows to a gigantic size.
Hydro Hog (Umibozu in Kakuranger), the Alien Rangers' Arch-Enemy on their home planet, was a variation. He was obese, but rather than being a Big Eater, he was more of a "Big Drinker", in that he was able to consume entire bodies of water (the size of lakes). Which is why he was such a deadly enemy to them, being of an aquatic species who depended more on water than even most beings.
In Supernatural the Leviathans' appetite for human flesh is so great that their entire Evil Plan consists of weeding out the competition and turning humans into docile livestock because they think our population is too low. Yes, six billion humans apparently isn't enough for them.
The first ten episodes of Ultraman Mebius give us Bogal, a rare female example. She's a vaguely snake-like kaiju who specializes in consuming all creatures on a planet before moving on to the next one. She has a particular taste for other kaiju, whom she awakens from underground or summons from space to be unwittingly eaten. In episode 9, she swallows Gudon and Twin Tail whole one after another!