Plot-Powered Stamina

Rather than being able to take insane amounts of punishment, someone is able to to carry on in a more mundane manner as long as the Rule of Cool, Rule of Drama, or Rule of Funny dictates. For example, police officers in most police procedural who seem to be able to stay awake for several nights and still chase the Villain of the Week, In games it is an Acceptable Break From Reality to keep the game from getting bogged down.

Drugs to do this are Bottled Heroic Resolve. If this is a character in general avoiding biological functions, it's Bottomless Bladder. When super heroes don't seem to need sleep, it's a Triple Shifter. If your mounted creature can do this, then it's one of those Automaton Horses.

Anime & Manga

 * Harshly averted near the end of Gundam 0083 Stardust Memory. The pilots are fighting non stop for hours, and Kou is seen injecting himself with what's probably a stimulant to keep himself going. It's also very visible that this is taking its toll on him.
 * Rock Lee from Naruto goes to great lengths in training so he can be a great ninja with only physical abilities. He gives himself insane rules, where if he doesn't finish the task he's on, he'll do something harder. For example: If he cannot kick a log 400 times, he will jump rope 500 times. It seems to have worked quite well.
 * Tohma of Magical War Chronicles Lyrical Nanoha Force. This was given a Lampshade Hanging in the third chapter when he realized how he's not tired at all despite running so long while carrying someone on piggyback and using high-level magic, with the implication that it's likely a side-effect of the Lost Logia he picked up.

Film
""That day, for no particular reason, I decided to go for a little run. So I ran to the end of the road. And when I got there, I thought maybe I'd run to the end of town. And when I got there, I thought maybe I'd just run across Greenbow County. And I figured, since I run this far, maybe I'd just run across the great state of Alabama. And that's what I did. I ran clear across Alabama. For no particular reason I just kept on going. I ran clear to the ocean. And when I got there, I figured, since I'd gone this far, I might as well turn around, just keep on going. When I got to another ocean, I figured, since I'd gone this far, I might as well just turn back, keep right on going.""
 * The excellent running skills of Forrest Gump nets him a spot on Bear Bryant's team and earns him a Medal of Honor in Vietnam when he rescues his entire unit (except for his Black Best Friend Bubba); after Jenny ditches him, he decides to go jogging and inadvertently starts a national trend, not stopping until quite some time later. (In his narrative, he claims to have stopped for food, water, rest, and bathroom breaks, but in the film edits it together so it looks like he just keeps going...and going...and going...)


 * And he starts out doing something between a jog and a sprint and ends rather trotting, with each new "year" showing him to slow down a noticeable amount...
 * Actually the reporters covering the story mention he only stops to eat and sleep.
 * This is said to be true of aboriginals in The Gods Must Be Crazy 2, where they can keep moving at a decent clip across long distances where Westerners would have stopped after less than an hour.
 * In The Graduate, Ben spends the last portion of the movie running like hell to stop his beloved's wedding, basically power-jogging nonstop for ages with only a pause to make a phone call. Nicely led up to throughout the film with repeated mentions of Ben's position in college as captain of the track team.
 * In The Two Towers, Aragorn and Legolas seem to be sprinting non-stop across miles and miles of land to chase down the kidnapped Hobbits, with Gimli barely keeping up and heavily winded. In the book, at least, it is mentioned that this is in fact abnormal and not just something they can all do all the time. It is apparently named "The Deed Of The Three Friends" and ballads are sung about it. The book also lets them rest a bit more than the movie, where Gimli states that it's been three days pursuit with no food, water or rest. In the book they at least pause so that Gimli and Aragorn can sleep while Legolas keeps guard, since his Elvish superpowers include the lack of a need to sleep.
 * J in the beginning of Men in Black runs down an alien (with some help from passing vehicles) known for its speed and is not winded at all after the chase that left the alien a little tired. This is part of what gets him into the MIB in the first place.
 * Toshiro Mifune's character in the Charles Bronson movie Red Sun spends all day walking across the desert, then says he'll keep watch overnight. When Bronson asks him why he's not going to sleep, he says he's already slept - "While walking". (Bronson does observe the following morning that for a man on watch, he did snore a bit.)
 * In Run Fatboy Run, this is how unathletic, heavy smoker Dennis finishes the marathon on a sprained ankle. Fueled by the fact that he had something to prove to himself, to his ex-girlfriend, and pretty much everyone else in his life except his son, who believed in him the entire time.

Literature

 * In Ranger's Apprentice, there's a note at least once a book that ranger ponies (and ranger dogs) can keep up their special ranger pace all day and not get tired.
 * The Aiel in the Wheel of Time might count seeing as how they can keep up with a horse while on foot and can do so for quite a while.
 * Trained humans can chase an unburdened horse until it dies of exhaustion. Keeping up with a warhorse carrying an armored knight is plausible, though Badass.
 * Robert Langdon from The Da Vinci Code apparently stays awake during the entire length of the book, finally crashing to sleep at the end.
 * In addition to his strength and fighting prowess, Fezzik of the novel The Princess Bride has arms that have inexhaustible stamina; the rest of his body can wear out, but his arms are always as fresh as ever.
 * The Dresden Files' Harry Dresden seems to fall into this trope under a certain interpretation of it. Most of the books involve him being slowly damaged far past the point normal people would be falling to pieces, and still fighting. By the end of most books he's a wreck, but with the bad guys defeated. He generally recovers but some wounds don't go away.
 * In one book, a physician points out how Dresden's body seems to not retain the wear and tear of his activities the way a normal person's would. Dresden concludes that a wizard's power gives them a very limited Healing Factor, which is probably responsible for their centuries-long lifespan.
 * To clarify the above, he can be injured, but when he heals, he heals all the way. Scar tissue heals at the same rate as normal injury, rather than staying static. The neat bit is that this is biologically plausible; there is a lab-mouse genetic line (known as MRL) that does the same thing.
 * The sons and daughters of Oberon in the Chronicles of Amber by Roger Zelazny. For example, Corwin and Random once fenced to exhaustion. Most people can fence at full pelt for a handful of minutes. Corwin and Random were still going strong twenty-six hours later. Corwin gave up so he could keep a hot date he had lined up.
 * In Romance of the Three Kingdoms, the top tier generals are noted for having jaw-dropping levels of endurance. One of the most famous instances is Zhang Fei's duel with Ma Chao—they duel for hours, even calling for torches once it falls dark. They keep going for so long that their seconds in command gets worried and has the armies pull back, at which point both complain that they could have continued fighting.
 * Beowulf is remarked as being able to swim for three days and nights underwater to reach the lair of Grendel's mother. This is just one of the hyperbolic superhuman feats attributed to him throughout the poem.
 * Averted, strangely enough, in the Harry Potter series. There aren't that many examples of grievous wounds or strenuous physical effort, but Harry himself suffers from the normal fatigue expected of a teenager. Especially prevalent in the Order of the Phoenix, where long hours of studying, practicing Occlumency, Quidditch workouts, and being woken up whenever Voldemort stubs his toe take their toll, causing him to fall asleep during the end-of-year O.W.L. exams, resulting in him tanking the History of Magic essays and leading directly to a laser-guided Catapult Nightmare. Poor kid needs to manage his time better.
 * Hermione also suffers from this when she takes every single class and elective in third year.
 * Subverted in Artemis Fowl. Several characters refer to being fatigued towards the end of the book (having been continuously awake for almost two days) but keep going.
 * The novella The Long Walk by Stephen King. The plot revolves around ordinary humans being able to go as far as possible. Failure is...unpleasant.
 * Justified in The Elenium. After a long day of travel, the knights discover that they are being followed by those who are seeking to kill them. Sephrenia uses her magic to cast a dangerous spell that simulates the effects of a full night's sleep. This allows them all to get to an inn where they can sleep safely. The spell is dangerous because it doesn't actually provide the rest that it simulates, so if used too often it can cause the caster to die from exhaustion.

Live Action Television

 * In one episode of The X-Files, Mulder spends several days doing a stakeout by himself.
 * Mulder does this more than once, actually. He's a chronic insomniac and is rarely seen sleeping in the show's nine seasons. He often goes several days without sleep. The cause for his insomnia is never given, though it likely has something to do with the high amount of stress in his life, his obsessive nature about his cases, and recurring nightmares about his sister's abduction. After Scullly is abducted in season 2, he spends the whole next episode not sleeping (at least a few days). In fact, when a detective suggests he finds a hotel in the area, Mulder says it isn't needed, as he "doesn't sleep anymore." His apartment doesn't even have a bedroom (or bed for that matter) until season 6.
 * Law and Order is inconsistent about this. Sometimes the detectives seem to stay up for an abnormally long time; other times, their boss insists they go home and get some rest.
 * Generally speaking, they appear back to back, such that the detectives are up for days and then told to get some rest. In the situations where they are up for abnormally long times, they are (depending on the writers) usually portraying the effects of sleep deprivation accurately: short tempers, lack of ability to focus, and so on.
 * The characters of 24 manage without sleep just fine for twenty-four hours plus however long they'd already been up. Speaking of which, season one started at midnight, meaning they were up for more like two days without sleep the first time around.
 * In season one, Jack Bauer does find enough time to get a catnap at roughly the seventh episode (when he's holed up in a building with a waitress he's taken hostage). He also finds time to eat a frozen dinner during his debriefing at CTU (in fact, the only other time he's shown eating is at the beginning of the fifth season). Aside from this, however, Jack and every other character on the show can function overnight or forego eating for extended periods of time. This appears to be the reason why most later seasons begin at 7 or 8 AM (making it so that the characters are really only staying up overnight) instead of late hour season starts.
 * It's canon in Star Trek that fresh, healthy Vulcans can charge their systems to go for weeks without sleeping. Used in the novels a lot when the crisis lasts for a long time.
 * Denobulans (e.g. Phlox in Star Trek: Enterprise) hibernate for a week or two per year, and are otherwise awake all the time.
 * Lost episodes 3x21 (The Greatest Hits) through 4x03 (The Economist) take place over a period of three really busy days and all main characters are shown to stay up on both nights with no signs of exhaustion by the end of the third day. Though the very first handful of episodes show a paraplegic man unexpectedly gaining his legs back...
 * Elliott from Leverage only sleeps ninety minutes a day.

Video Games
Please only list subversions and aversions here; games with Sprint Shoes or a Sprint Meter go into that particular category.
 * Grand Theft Auto: Vice City, introduced a hidden stamina characteristic, but an exploit (tapping the run button instead of holding it) allowed infinite running. This was corrected for the following games.
 * When Mario and Sonic the Hedgehog are at the Olympic Games, neither is capable of running the 400m or 440m hurdles at a sprint. They get tired if they try.
 * Bully will allow Jimmy to get to bed around 19:00 or so. At 01:00, he's dragging. At 01:45, you're partway into Interface Screw. And at 02:00, you sleep wherever you are, hopefully inside a building. No matter what. Bedtime, James.
 * Dead Rising and its sequel both have the main character leading a physically very active life for three days straight (possibly a full week in the first game), without a wink of sleep. Food, drink and bathroom breaks are available in quantity, though.
 * Fallout: New Vegas averts this in Hardcore mode - going for too long without sleeping (or food or drink, for that matter) will increasingly weaken your character, and eventually kill them if allowed to go long enough.
 * Dead Island. Averted hard. Everything takes stamina, including attacking with a melee weapon, so you can forget about the "melee spam" tactic seen in games like Left 4 Dead. This becomes a real issue when you're facing multiple zombies.
 * Played with in Uncharted 3. One level consists mostly of Nate staggering around the Rub' al Khali desert, growing more tired and thirsty the whole time. By the time he reaches a Ghost Town, he can barely stand. Just a few minutes later, he gets into a gunfight with no problem whatsoever.

Webcomics

 * After being forced to leave Azure City, Vaarsuvius of the Order of the Stick has stopped “trancing,” leaving him/her/it rather haggard. This was recently revealed to be due at least in part to.
 * During the DARE To Resist Drugs and Ninja Violence arc in Dr. McNinja, the Doctor realizes that it's been almost two days since he ate or slept while dealing with a random ninja mook. The mook tries to laugh it off, but it's made the doctor a bit cranky.
 * During the DARE To Resist Drugs and Ninja Violence arc in Dr. McNinja, the Doctor realizes that it's been almost two days since he ate or slept while dealing with a random ninja mook. The mook tries to laugh it off, but it's made the doctor a bit cranky.

Real Life

 * Pheidippides was said to have run 150 miles (Athens to Sparta to Marathon) and then 26 miles (Marathon to Athens) to bring word of victory at the Battle of Marathon. The modern concept of the marathon run is named in honor of this achievement.
 * This is humanity's "superpower" compared to most of the animal kingdom. While many prey and predator species are great at sprinting, and can reach speeds a human couldn't possibly hope to match without a vehicle, they can only do that for a short time. Humans, meanwhile, have the endurance to just keep going. There are tribes in Africa that hunt by doing this, essentially "chasing" the prey at a brisk walking pace until the target has exhausted itself. In fact, no animal on Earth can outrun a human in long distance running. None.
 * Herschel Walker, former NFL running back, may be the single most determined man on the planet. In place of lifting weights, he chose to use basic push ups and sit ups to keep his body in top form. As of 2010, his daily workout still consists of 3,500 sit ups and 1,000 push ups.
 * Just to break that down with some impressive math skills, that means that, assuming he does one sit up every second, he would have to be doing sit ups non-stop, once a second every second, for almost an hour to meet this regimen. Most people don't do that many in a year.
 * See also: Humans Are Special
 * Dean Karnazes. Just take a look at his article on Wikipedia.
 * Horses not only have a unique physiology that allow them to run longer, domesticated, trained horses lack the survival instinct to not run themselves to death if pushed to do so.