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.
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.
The 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.
It was noted at the Time that the deep region of rock where Xanth abided had soaked up so much magic from his long stay to function as a battery. (There's a village which falsely believes they act as the source of the realm's magic by creating storms to spread magic-charged dust which comes up from the rock nearby - they have no idea of its ultimate source.) Demons were established at the time as already living deep underground where magic was already more powerful due to this, and their personal power somewhat dependent on how deep their society permitted them to reside. Taking in refugees from above would probably let most of them survive during Xanth's absence, or at least not sustained irreversible damage.
The black mages and many other monsters in Final Fantasy IX are spawned from concentrated Mist, which is a decidedly evil fog composed of souls of the dead that have been blocked from going to the afterlife.
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 Zerg in StarCraft use minerals and vespene gas as resources by metabolizing them.
The main character, splicers and little sisters in Bioshock.
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.
The Elders in lonelygirl15 need to receive trait positive blood transfusions on a semi-regular basis to survive.
Inverted in Futurama: Nibblonians excrete Dark Matter, which is used as starship fuel.
At least it was, until it was rendered inert in the third movie. Now interstellar travel is powered by whale oil. It's debatable whether this or Nibblonian poo is the more ludicrous fuel source.
The energon in all incarnations of Transformers. It powers their weapons and ships and is also their currency and food. This means Transformers eat money and starship fuel. And in every series except for G1 and Ri D, it's a natural resource that the Forever War has made quite scarce, and making substitutes either is impossible or what you get comes with nasty side effects. Drugs Are Bad, mmmkay?
In those series, though, it was possible to create energon from other energy sources. For them that makes it easy: oil, gas, etc. is a handy source of food and fuel. It makes them Phlebotinum Munchers to us instead. Many a G1 episode and comic revolves around raids on everything from oil wells to hydroelectric dams to concerts (the music is somehow made into energon, causing it to sound just horrible to the listeners.) for energon.
In Aladdin: The 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.
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 known 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 competitors discovering it and doing so anyway. And any researcher who discovered a cure for any form of these diseases would have no reason to hide the cure, because revealing it would make them one of the most famous and wealthy people in the history of the planet.