Perpetual Motion Monster

""My lord," it was the master of the goblin blacksmiths, offering to build the king a new army, a mechanical army "seventy times seventy soldiers that can never tire, never know hunger or pain, and never be stopped.""

- Hellboy II: The Golden Army

This is a type of monster that is immune to starvation and dehydration, it may not even have to sleep or breathe. Much like the Energizer Bunny, it just keeps going and going and going. Perpetual Motion Monsters are either explicitly supernatural, a set super advanced Mecha-Mooks, or both.

Science savvy characters may discuss how implausible it is that the walking dead in a Zombie Apocalypse, despite craving brains, can keep walking 24/7 for years or longer without any kind of sustenance. Compounded by that fact that though decayed they never actually rot enough to stop posing a threat. Frequently, The Professor / Mad Scientist will fear (or marvel) at the potential these thermodynamic law breaking monsters represent. This is the whole idea behind undead armies in any setting—they are weak but fearless and while slow, they can march 24/7 with no supply lines, all while assimilating the enemies' fallen.

This is usually a Justified Trope for Ghosts, Dem Bones, and Elemental Embodiments since they aren't really biologically based, so they don't need traditional food sources. Although, they may need some other form of energy or material as a Power Source (like prayers or lighter fluid), thus averting this trope. For Mecha-Mooks and other technology based creatures they usually incorporate some near infinite Power Source (or a means to tap into an external one) and some form of Regeneration.

It's worth noting that a character with the right type of Immortality who eats and drinks can still be a Perpetual Motion Monster—or rather, a Perpetual Motion Man. Their form of immortality specifically preventing them from dying due to starvation and dehydration (though they probably won't enjoy it). Such a character can make for a truly Implacable Man—nothing can keep him from his goal, not even the ravages of time!

For extra threat, the Perpetual Motion Monster is also usually unaffected by dismemberment (except for the "annoyance" of a lost limb, though a needle and thread can solve that). For extra extra threat, it's also a Super-Persistent Predator; since being a Perpetual Motion Monster means it doesn't actually need to eat except for the pleasure of it, it can afford to go to the ends of the Earth in pursuit of that one tasty hero-sized morsel.

Compare Automaton Horses (not the mechanical variety), where this is noted as one of the features that make fictional horses unusual. Compare Forgot to Feed the Monster when this is averted.

Related to The Insomniac type 4 (doesn't need to sleep).

A Sub-Trope of The Needless.

Anime and Manga

 * The synthetic humans in Biomega come pretty darn close. They can live for months without food and for weeks without water and not lose efficiency.
 * Androids 17 and 18 in Dragonball Z are "infinite energy models" according to their creator, Dr. Gero. Androids 19 and 20 must absorb energy from people instead. This "Infinite energy" is also their weakness, since they can't exceed their power level unlike Cell or Gero.
 * Alucard, a vampire, in Hellsing was sealed in the Hellsing estate for decades without blood and was still "alive". Granted, greatly weakened, and dessicated into a husk, but he still woke up when exposed to blood.
 * Chiropterans in Blood+ won't die from starvation, as happened to one imprisoned in a concrete block in Russia. It was emaciated but still awake and capable of killing.
 * The eponymous warriors in Claymore do not need to eat or drink except in small doses. Though, when they awaken, they eat human flesh regularly, but can go without for a long time (several years), but it does weaken them...
 * The Angels in Neon Genesis Evangelion are explicitly stated to have an infinite power source in their bodies: the S2 Organ. Therefore, while alive, they have no need for sustenance, rest, etc. and are effectively immortal, though they can still be killed if damaged enough.
 * The Titans from Shingeki no Kyojin. While lack of sunlight and fatigue can slow them down, they do not age, sleep, or thirst and do not need the human flesh they eat. They even regenerate biomass instantly and out of nowhere while thriving.

Comic Books

 * Reed Richards in Marvel Zombies cites this trope as his justification for believing the zombie plague is the next step in evolution. He then proceeds to In this case, Reed Richards is Genocidal.
 * Scrooge McDuck once had an immortal zombie go after him for very long time, often walking nonstop across oceans, being frozen in ice for long time, and so on.
 * The zombies in The Walking Dead are very much Perpetual Motion Monsters.
 * For X-Men foe Juggernaut, this is basically his power (mystical power in the comics, mutant power in the movie).
 * Taken to an interesting new height in Fear Itself. While possessed, he truly becomes unstoppable. At some point in the event, he calmly walks to San Francisco from a dozen miles away, while the X-men try a bajillion plans to stop him. Teleporting him away does nothing, he just reappears instantly. Digging a giant trench in front of him does nothing, somehow he strolls calmly across thin air!
 * Willy Pete from Empowered is an incredibly powerful fire elemental that eats superhuman flesh because he likes the taste, and because super-strong flesh is the only food that his mouth won't instantly incinerate. Being a fire elemental, he doesn't actually need to eat.

Film

 * The eponymous army in Hellboy II: The Golden Army is a positively inhuman combination of perpetual motion monster, The Juggernaut, and regenerating. It was an ancient weapon Gone Horribly Right to the point the elf king who commissioned it sued for peace after it massacred a human army.
 * The monster from the movie version of Peter Benchley's Creature survived locked in a cage on the sea floor without any food or room to move for decades without any debilitating effects. The book version averts this by having it stalk out of its cage in a deep sea trench ever so occasionally.
 * The original Terminator movie made the eponymous cyborg sound like this trope, until the second film subverted it by revealing that his power cell would eventually run out.... after 120 years.

Literature

 * In Robert E. Howard's Conan the Barbarian story Black Colossus there's a giant venomous python which slithers out of a 3000 years old tomb and is still lively and in top shape.
 * In The Lord of the Rings there's the Watcher in the Water, a massive squid-like beast living in the pool of water just outside Moria. It had been driven from the deeps of Moria into the flooded valley as a guardian and to trap the dwarves inside Moria. A creature that big just hanging around in caves needs to have SOME of this going on though.
 * In The Zombie Survival Guide zombies are explained by the virus which creates them replacing their mitochondria and taking over respiratory functions so they no longer need to eat or breath (...somehow) and slightly more plausibly, delaying decomposition by protecting the body from rotting as the immune system would have. The later part of the trope is also averted, since zombies do rot away after a few years, unless they're in arid environments or end up being frozen.
 * Not "monsters" per se, but Discworld Golems just keep going and going and going and going. They're used for menial, tedious labor typically, since they don't have to sleep and, for the most part, enjoy it as much as they can enjoy anything. They even use this as a form of passive-aggressive protest via Literal Genie; they're smart enough to take initiative and can read the intent behind orders, but if you mistreat them, they're liable to fight back by doing exactly what you say, constantly, until someone figures it out and tells them to stop. This can mean that the golem you asked to "pump some water" doesn't stop until your shop's street is partly underwater.
 * A more traditional version, also a golem, is Mr. Pump in Going Postal. As Moist's parole officer, it's explained that even though he can only walk while Moist can run, get a horse, or a cart, he will never tire, and never stop until he catches up to him. After one demonstration of this, Moist gives up on trying to run away.
 * In The Synthetic Men of Mars, a malfunction at an already imperfectly working cloning facility produces a constantly growing mutant entity that consists of a huge blob of human flesh and random body parts. It's stated that if it hadn't been fire-bombed from above until there was nothing left, it could have grown forever by eating itself. Just think of the potential applications of something like that on a starving planet.
 * The zombies in Diario de un Zombi, minus some very gradual wear and tear.

Live-Action TV

 * The Jem Hadar in Star Trek: Deep Space Nine are genetically engineered so that the only source of nourishment they need is Ketracel White, a narcotic which keeps them loyal and without which they die after going violently insane. On top of that, they are conditioned to be unwaveringly loyal (though this has proven to be slightly unreliable, hence the White as a secondary measure).

Mythology

 * The serpent that guarded the Golden Fleece, which never slept or left the tree except when drugged.

Tabletop Games

 * All creatures that lack a Constitution score in Dungeons & Dragons, such as constructs and undead, don't need any rest to remain operational or any external ressource to sustain themselves. As a drawback, they can't recover from damage naturally, unless they have the fast healing ability, which is the case for a few of them.
 * While similar, living constructs, the Warforged in particular are this as well, though it was changed to needing down time similar to sleep, though less of it than other races.
 * Pathfinder has a borderline case with clockwork constructs that need to be wound with special keys every few days to keep working, and only intelligent clockworks can wind themselves.
 * Artifacts in Magic: The Gathering usually have this quality, as do a lot of undead. Phyrexians in particular are prone to combining the two.

Video Games

 * Necromorphs in Dead Space don't need to eat, drink, sleep, or breathe. Have fun!
 * The Dahaka from Prince of Persia fits the role.
 * Dwarf Fortress actually has tags for these including [NOEXERT], [NO_EAT], [NO_DRINK], and [NO_SLEEP]. In-organic creatures like bronze colossi and iron men don't need any, while Goblins just don't need to eat or drink.
 * In the case of Goblins, their lack of thirst and hunger is only to avoid a Game Breaking Bug.
 * Corprus infectees in Morrowind suffer massive, uncontrolled muscle growth, to the point where they can apparently survive by cutting off their own tumours and eating them.

Web Comics

 * The Uncroaked/decrypted in Erfworld have zero upkeep.
 * Interestingly, the latter still eat and drink, and are provided with what they need as if they had their usual upkeep cost (in the textual interludes, Parson tried Decrypted archon rations). Something outside the known forces of the world is evidently picking up the tab.
 * The God Tiers in Homestuck are likely this. A player who reaches god tier can only die a heroic or just death. Death by starvation/thirst probably doesn't count.
 * They could go on a hunger strike, or be executed by starvation.

Web Original

 * In "Volume 2, World of Remnant 3" of RWBY, Grimm are suspected to not need food to survive.