Phlebotinum Muncher

Basically a creature which needs whatever Phlebotinum is being used in the story to survive. Often developing an insatiable Horror Hunger for the stuff. This can vary from a creature that eats Green Rocks to a monster called into being by Aesoptinum. The inversion of this trope is Phlebotinum Dependence - the character despises their dependency on Phlebotinum.

Anime and Manga

 * Dirty Pair: Project EDEN had this as a major plot point; the Sadinga monsters fed on Vizorium ore (warp drive fuel), and the fossils they were revived from were being mined for said ore until the Evilutionary Biologist came along.
 * Homunculi in Fullmetal Alchemist are addicted to the Red Stone and munch on the stuff for extra 'lives'. Red Stones are created by sacrificing human lives and are needed to create the phlebotinous Philosopher Stone, which basically enhances the magical powers of alchemy. In the original manga, the Red Stones simply don't exist. The Homunculi rely directly on Philosopher's Stones (yes, plural) to provide their limited immortality.

Comic Books

 * There was one Superman story where he arrived at a moon of Krypton (long story short, it drifted away hundreds of years ago) and had to use kryptonite to prevent its Uranium core from exploding. On his search for enough kryptonite he came across a (space)monster that fed on it. He managed to save the planet, but since it was now made of kryptonite, he could never go there again.

Literature

 * Larry Niven's The Magic Goes Away stories had dragons, mermaids, were-creatures, gods and such that metabolized Mana. This was a kind of environmental metaphor; when human wizards started using up the mana faster than it could regenerate, all the fantastic creatures went *poof*.
 * The ultimate weapon of the setting was a magic disk. Powered by a simple propulsion spell with no speed limiters (and a secondary spell to keep it from tearing itself apart), it simply spun around uselessly and thus wasted all the Mana in the area. Wizards were left powerless, werewolves lost their "were-", and ageless beings suddenly began feeling their age. This is the origin of the Magic: The Gathering card "Nevinyrral's Disk", which does pretty much the same thing.
 * Something similar happened in Xanth when the Demon of the same name temporarily absented himself from the realm.
 * In addition, when Demoness Metria traveled to Mundania, she had to be accompanied by a guy whose talent was to project an 'aisle' of magic around him whenever he was in Mundania, because a minor demon's Mundane form is a dust devil. How the minor demons survived the Time of No Magic (when Demon Xanth left) is a Fridge Logic question.
 * Because they hadn't been introduced to the series yet? Alternately, possibly Hell isn't part of Xanth.
 * Ungoliant in The Silmarillion pretty much subsists on shiny elf artifacts.
 * Discworld. Dragons eat magic, and salamanders absorb the magical octarine frequency of light.

Tabletop Games

 * The atog from Magic: The Gathering eats magical artifacts, and its various relatives eat other magic-related things: the auratog eats enchantments, the chronatog eats time (you can give it a big stat boost by skipping your next turn), and the atogatog eats other atogs.
 * Magic also had a reference to "The Magic Goes Away" in the form of Nevinyrral's Disk--they were more willing to pull Sdrawkcab Name tricks in the earlier days of the game.
 * Most creatures in GURPS that use magic naturally have a dependency on background Mana and will rapidly die if totally deprived of it.
 * Dungeons and Dragons has had a number of creatures that feed on magic, such as the Disenchanter.
 * Shadowrun. Strain III bacteria eats magic and lives in astral space. It can drain magic out of an Awakened creature, causing it to weaken and die.
 * Skaven Grey Seers or Warlocks from Clan Skyre can munch down Warpstone in order to fuel their spells. Can turn them into Chaos Spawn though.

Video Games

 * The Worm/Metroid Prime/Dark Samus from Metroid Prime (and other Phazon enhanced creatures) needs Phazon to live.
 * The black mages and many other monsters in Final Fantasy IX are spawned from concentrated Mist, which is a decidedly evil fog composed of.
 * Rock/Ice/Lava Monsters in Lego Rock Raiders eat energy crystals, and will destroy your buildings to get at them. If destroyed the crystals they have eaten can be recovered. Slimy slugs are similar, except they suck the energy out of them instead.
 * World of Warcraft has mana wyrms and arcane elementals that feed on Mana, often appearring in locations with large amounts of loose mana.
 * The Adephagos of Tales of Vesperia gets summoned into the world by an overflow of Aer, a magical substance that all the machines in the world consume to function.
 * Do the Zerg in Starcraft count? The way they use minerals and vespene gas as resources almost makes it look like they eat the stuff...
 * It does - they metabolize it.
 * The main character, splicers and little sisters in BioShock (series).
 * Although this is borderline, since they need it to make themselves powerful enough to survive rather than to live.
 * Only at first: long term use (enough to drive you mad, possibly semi-randomly mutate you and get you to the point you're referred to as a "splicer") gets you psychologically dependent on it; keep going, and you need fresh intake of Adam and the occasional plasmid just to keep your body from completely breaking down into a puddle of goo. Fortunately, THAT pleasant experience doesn't show up anywhere in the games.

Web Comics

 * The Inexplicable Adventures of Bob: Thanks to a botched scheme by her clone Golly, Molly the monster now has a second clone named Jolly who is the size of a small mountain. Considering what Big Eaters Molly and Golly are, Jolly's potential food intake beggars the imagination. This is Handwaved with the explanation that, among her various bionic implants to help her move and respirate at such a huge size, she has a "Phlebotinomatic Food Synthotron."

Web Original

 * The Elders in Lonelygirl15 need to receive trait positive blood transfusions on a semi-regular basis to survive.

Western Animation

 * Inverted in Futurama: Nibblonians excrete Dark Matter, which is used as starship fuel.
 * The energon in all incarnations of Transformers.
 * Although, to be fair, in most they can synthesize it from any available source of energy, so it isn't exactly rare phlebtonium, except for all those poor stupid fleshlings who don't know how.
 * In the Aladdin series, the resident Phlebotinum Muncher is a one-eyed creature called the thirdak, which eats magic. It tried to eat Genie and managed to eat half of Carpet.

Real Life

 * What would you need with a complex organic molecule, acidic hydroxide and an oxidiser? Why, you must eat sugar, drink water and breathe oxygen to live.
 * Long term alcohol addicts might find that withdrawing cold turkey can kill them through shock. A theoretical possibility of death also exists with benzodiazepines and barbiturates, because withdrawal from them can cause seizures, but alcohol withdrawal is the only withdrawal syndrome to have actually killed anyone.
 * A common accusation is that drug companies will never cure cancer/AIDS/etc. because cures would eliminate demand for expensive treatments. A related accusation is that drug companies are in fact spreading those same diseases to make the entire world dependent on treatments. They technically come about because of unrealistic expectations. For example; Cancer is in fact not a disease, but many, and a cure for one type would not likely have an effect on any other type. Quite a lot of research is also done by non-profit organisations who can only really "make" money in the form of further funding (although this isn't their goal anyway) by coming up with results and would have very little reason to keep it to themselves. Similarly, even a "for profit" company would have to sell a cure or risk their copetitors discovering it and doing so anyway.