Czeslaw Meyer from Baccano!. After 200 years of being pointlessly tortured, he's very careful about who he should trust. Especially when it comes to other immortals.
In the anime of Desert Punk, Kanta ends up being this to a disturbing extreme. During the second season, there are hints due to his views on the world as a survivalist and realist. It all eventually leads to Kanta becoming a government agent and hunting down his friends. He much prefers that people stand on their own two legs with just enough for survival, which the corrupt government does manage to do...barely to the idealist movement his friends joined. Oh, and he killed almost an entire family, the same family that made his wench, because they saw his face and could be a problem down the line. Oh boy, did he ever cross the Moral Event Horizon. He even seems to admit it.
Y: The Last Man. The "Sons of Arizona" are convinced the death of all the men is a federal government plot and beat up Dr. Allison Mann in the belief that she's somehow involved.
American Flagg has the fascist American Survivalist Labor Committee (A.S.L.C.), which teams up with the Gotterdammercrats, the more "respectable" party of Illinois Nazis, to take over Chicago.
The Life Foundation was an organization that appeared mostly in Spider-Man comics who had a demented view of this. They were certain that society would eventually collapse and were survivalists, but had no intention of actually being uncomfortable when it happened. Certain there were other rich and selfish people with this view, they built large, secret enclaves designed with luxury in mind (basically, town-size shelters with resort themes). The most sinister thing about this is their various ideas for keeping others out, including robbing militia for weapons (and then kidnapping the hitman Chance and trying to get the secret of his weapons out of him) and hiring mercenaries to undergo surgery to make them super-strong (not telling them it would turn them into Brainwashed slaves). By far their worst mistake was trying to use the Tri-Sentinel. (Not only a Sentinel, but three Sentinels merged together by Loki's magic in order to destroy New York during the Acts of Vengeance. Suffice to say, it was a bad plan.)
Huey was like this in The Boondocks. To give one example, in one series of strips, he was certain a bird flu epidemic would cause a plague that would destroy America, and stockpiled 18 months worth of food to prepare, saying he wouldn't even share with his brother when it happened. (Given that the bird flu had no cases outside of Asia, you can only find this rather absurd now along with a lot of his paranoia in the strip.)
The movie Resident Evil 3 opens up with a family of Crazy Survivalists trying to rob Alice. Poor, poor crazy survivalists...
Harlan Ogilvy in 2005 The War of the Worlds, a paramedic holed up in his cellar whose mind began to deteriorate after his wife and child died in the invasion. Tom Cruise's character is eventually forced to kill him to prevent his ravings from attracting the invaders.
If you've ever heard the Jeff Wayne musical version of War of the Worlds, there's also the young infantryman who decides that the best thing to do is hide out in a cellar and carve out a brand new underground city. His glorious project is, by the time the protagonist reaches him, a 10 ft deep hole in the cellar wall and yet he's making plans for playing cricket underground, defeating the invaders, and starting again. With "just a handful of men".
Burt Gummer from the Tremors movies and TV series is a somewhat rare friendly, even heroic version of this. He actually helps out the rest of the town when they need it, since he's the only one with enough guns to fight the graboids. ("Well, I guess we don't get to make fun of Burt's lifestyle anymore.") Through the second and third movies he adds ever more powerful weapons to his arsenal (including an anti-tank rifle and an anti-aircraft cannon). By Tremors 3 he stops being this and becomes more Properly Paranoid, seeing as he's already lived through two monster invasions. By the time we get to Tremors: The Series he's pretty much become a professional monster hunter.
Note that Burt always follows proper gun safety, unlike how the typical gun nut is depicted. One notable example: At one point he gives a revolver to Melvin to convince him to move to a safe-point. Despite knowing that he'd deliberately handed Melvin an unloaded gun (Burt was smart enough not to trust a jerk like him with a loaded one), when Burt takes it back from Melvin he still flips it open and re-confirms the chambers are all empty... which is exactly what you're supposed to do any time you pick up a weapon.
The third movie, Dawn Of The Dinosaurs, features Buck, a weasel stuck in a Lost World full of dinosaurs. He has an Ahab-like obsession with a giant dinosaur who took his eye... and clearly took his wits along with it.
Manny: When did you lose your mind?
Buck: Ah, about three months ago, actually. I just woke up one morning married to a pineapple! An ugly pineapple. Ahh, but I loved her...
The Robin Williams / Walter Mathau film The Survivors poked fun of the survivalist craze (emphasis on "craze") that peaked in the mid eighties just before the end of the Cold War. William played Donald Quinelle, a hapless yuppie who turns into a rabid survivalist after losing his job.
Bobby Lee Swagger from Shooter lives in isolation at the mountains and has rather extensive field training.
Everyone in Carriers is a crazy survivalist when an infection threatens to wipe out all of humanity.
In The Book of Eli, the titular character comes upon a sweet old couple living in a farmhouse in the middle of the wasteland who take him in. However, turns out they're not only this, but a Cannibal Clan as well. Before they can kill and eat him, though, the Big Bad shows up, and they team up with the hero in the ensuing battle.
The original Highlander film featured one of these as an ex-military, gun-toting vigilante who witnessed one of the Kurgan's modern-day duels. He shoots the Kurgan like Swiss cheese. Having killed the apparent murderer, the survivalist goes to look, and gets skewered, lifted off the ground on the Kurgan's sword. He (barely) survives, and probably became a Watcher if series mythology figures in.
The protagonist of Take Shelter begins to show shades of this when he secures a risky loan just to buy an expensive shipping container, all in order to expand the shelter in his backyard in preparation for the imaginary storm that is to come.
The book The Postman states that America as a nation scraped through World War III and even appeared to be on the road to recovery... only to be permanently torn down by attacks by anarchic survivalist militias. Though it's admitted that the Holnists are more like Social Darwinists who want to be feudal lords rather than "true" survivalists, but the term has been permanently associated with them by the survivors.
Subverted in World War Z, where these guys are officially referred to as LaMoEs — Last Man on Earth — and came in two varieties: The ones that are still sane, and—after the initial confusion—welcome the army, are referred to as Robinson Crusoes. The second type, which the narrator notes is the type that the rank and file actually do refer to as LaMOEs, are the ones who either went a little too mad, or just got too used to their newfound lifestyle and didn't want to reintegrate into society.
Inverted in The Survivialist, the 1980's After the End action-adventure series by Jerry Ahern, whose protagonist (a doctor and former intelligence agent) is a good deal more rational and clear-thinking than most of the people he encounters. But then Ahern deliberately set out to avert the popular image of the crazy, right-wing survivialist (the protagonist's closest friend is Jewish, and his Unrequited Love is a female communist agent).
In Harry Potter, Alastor "Mad-Eye" Moody's Catch Phrase is "Constant vigilance!" His crazy magical eye that can see through most solid objects and magical barriers (like Harry's Invisibility Cloak) only enables his Crazy Survivalist behavior further. Though he has good reason to act this way: he's an Auror (Dark Wizard fighter) and has lost a leg, an eye, and a chunk of his nose on the job. And possibly, at one time, a buttock.
Subverted in the 1632 short story "Curio & Relic". Paul Santee has a lot of the common Crazy Survivalist traits. He lives on his own on the outskirts of town, he's a Vietnam veteran, and he has a lot of guns. Fortunately for Eddie Cantrell, Santee's actually not crazy at all, he's just not a people person. As for the guns, he's a registered collector and seller of antique firearms, so all the guns he has are legal. Once the situation is explained to him, he's more than happy to donate his Survivor Stash to the new army, and even gets the job of "Chief Weapons Scrounger".
In Eon, it's mentioned that these guys didn't last long after the Death. In fact, they were abhorred for their unwillingness to help others.
Live Action TV
A Crazy Survivalist rescues Kim Bauer from a jaguar in 24 then tries to convince her that Los Angeles has been nuked and she should stay with him in his bunker forever.
MacGyver has been known to pull some Crazy Survivalist tricks out of his hat when needed.
Jim Taggart on Eureka. Sometimes he's usefully crazy, other times, he's just running around in the woods naked for a reason known only to himself.
Alyx from Dead Set. She's deadly accurate against zombies with a gun, usually goes alone, and only takes one other survivor with her because he has supplies she doesn't. However, she develops a soft spot near the end which ends up killing her by helping Riq.
In Supernatural, FBI agent Hendricksen (quite accurately) profiles the Winchester clan this way. However, he's wrong in his speculation that John might have been a white supremacist and child molester.
A serial killer/kidnapper pretends to be this (very convincingly) so he can play out his Adam and Eve Plot fantasy with his surviving female victim in Medium
Rousseau from LOST, due to being stranded on the island for sixteen years.
As of season 6, Claire too.
Highlander: The Series has Methos, who's survived for 5000 years by being one step ahead of the other guy (or girl). He never puts himself in unnecessary danger and always has a way out.
When the Star Trek: Voyager crew traveled to the 20th century, one subplot was Chakotay and Torres being captured by these.
In one episode of The X-Files, a survivalist assures Mulder that not all survivalists are violent paranoids who hate the government. "But we are."
In "Shelter Skelter," an episode of the '80s revival of The Twilight Zone, a crazy survivalist (Joe Mantegna) and a friend find themselves trapped in his shelter, believing themselves to be sole survivors of a nuclear war. Turns out a nuclear explosion did occur, but due to an accident at the nearby airbase. The reason the radiation levels haven't dropped are because the town is now sealed under a concrete dome.
In "The Release", an episode of the short-lived Animorphs TV series, there was Mr. Perkins, a high school teacher and former Controller who eventually runs off into the woods once he's found out. Unlike many other examples of this trope, Mr. Perkins was light on the crazy and heavy on the survivalist, rather than the other way around.
By the third season of The Walking Dead, Morgan (from the first episode) has become this.
Project Zomboid: The human enemies in the game are this. You yourself can become this.
In Dead Rising, the protagonist Frank encounters a crazed redneck survivalist holed up in a gun store who shoots at him when he gets too close (it takes place in a cutscene, so the player doesn't really have a choice).
He is actually surprised when you want guns enough to shoot HIM dead!
The actual effect is that the guy is crazy enough to not trust anyone with his guns, and kills anyone that approaches. When you kill him, he questions if you're crazy enough for guns to kill people. Bastard.
The Halls a.k.a. the family of snipers have this going on as well. Well, not Thomas, but otherwise...
The Spartan Federation, an entire society of these guys, are one of the factions in Sid Meiers Alpha Centauri. Humorously, they're the only faction canonically confirmed to have been completely eradicated.
The four protagonists of Left 4 Dead all have a touch of this.
The sequel gives us minor character Whitaker, a gun store owner who barricaded himself in a shed on the roof with more food and ammo than appears in the rest of the game combined. He forgot to store drinks, though, resulting in a Fetch Quest for you.
Father Grigori of Half-Life 2's Ravenholm certainly fits the trope. The sole remaining human resident of Ravenholm, armed with his trusty rifle Annabelle, he sets traps all over the place to tend to his "flock" - consisting entirely of assorted headcrab zombies that are all that remain of the town's residents...
Unlike many crazy survivalists, Grigori is actually a very helpful Crazy Awesome character, who saves your life several times and even has the common decency to provide you with your very own shotgun so you can help with him with his good work.
Hell, Gordon himself has turned into quite the crazy survivalist after the resonance cascade. He has somehow suppressed his basic human needs to eat, drink and sleep. He's been through situations that would certainly cost most people their sanity. Plus, he carries a full arsenal on his person at any given time, including but not limited to a crowbar, a pistol, another better pistol, a submachine gun, a shotgun, a crossbow, a full set of grenades, a missile launcher, and depending on the game, a whole assortment of more exotic guns, both large, small and very, very strange. Of course, he's being Properly Paranoid, but that's no assurance he's sane. Not having muttered a single word of complaint throughout the whole ordeal doesn't really help his case.
The first F.E.A.R. game had a fat guy whose name escapes me at the moment. He was always locking himself in (and you out) to save himself from the bad guys at your expense. He gets killed at the end although in the un-canon expansion Extraction Point he is shown to have survived it and returns to do the same Crazy Survivalist act all over again.
Jenkins from Red Faction: Guerrilla, complete with check shirt , puffy vest and cap. While the player performs Rail Shooter missions, popping rockets off at EDF assets from the back of Jenkins' trike-car, Jenkins relates his survivalist philosophy. He wants total independence of Mars from "them" (Earth), to the point of inventing his own "Mars words" to replace English and trying to "teach" himself to breathe carbon dioxide. Upon blowing up a target he will frequently cry out that he is "Clean and Righteous." At other points he announces that while everyone thinks he is crazy, he is the only sane man, and that "they" are always watching. Jenkins eventually goes right over the edge, deciding the Earth forces exist because of the rebellion, so the only way to be Clean is to betray the rebellion.
Plants vs. Zombies features Crazy Dave, your neighbor, who drives around with a station wagon full of lethal seeds, wears a pot on his head, and speaks in a Sims-like garbled growl.
Most of the NPCs in the Fallout games. Fallout 3 is more optimistic and has more than its fair share of caring, sharing types - encouraged by morality cheerleader Three Dog - but most of the communities you meet are isolationist and will only look out for themselves, and it is also implied that most individual Wastelanders are that way too. The Outcasts even left the Brotherhood of Steel for not being Crazy Survivalistenough.
Subverted by a former Marine in the Honest Hearts DLC for Fallout: New Vegas; who, despite surviving unbelievable wasteland conditions and human atrocities, becomes a benevolent Stealth Mentor to a group of kids, who eventually become The Sorrows. read his exploits here.
Although being prepared for the nuclear blasts, mutant invasion, monster attacks, and government supersoldiers enforcing their way is nothing more than common sense in the world of Fallout. Because, you know, all things Crazy-Prepared people prepare for already happened there and most of them are order of the day.
In Rogue Survivor, you can play your own character this way, especially as the most recent versions of the game allow you to murder survivors who intrude in your safe house.
Planescape: Torment has the aptly named Paranoid Incarnation, a past version of you who was both quite insane and absolutely, screamingly terrified of enemies lurking in every corner trying to "steal his body"; he had a habit of strangling people when they gave him news he didn't like and using his own detached arm in combat (since he always had it on hand, so to speak). Nonetheless, despite or perhaps because of his crazy, he left many clues for himself that prove helpful to you - provided you survive whatever spectacularly lethal defences he set up around them. And then successfully decipher his ramblings. Which may be written in a dead, obscure, complicated language known only to him and the guy who taught it to him, whom he strangled. He - well, it was an apt name. However, he is ultimately revealed to be a tragic character, much like you; waking into a strange world that showed him nothing but hatred and fear for reasons he couldn't remember. He's relieved to the point of tears when you finally convince him he doesn't have to be afraid, and willingly joins his mind with yours to find some peace.
The Sims 3, of all games, features a premade character like this: Hunter Cottoneye, who lives in Riverview. He lives in a bunker, wears all camouflage and has the Insane, Neurotic, Loner, Mean-Spirited and Angler traits.
In Assassin's Creed: Revelations, Desmond Miles would tell people who asked about his history that his parents were these. It's true from a certain point of view: his family lived on a farm off the grid in the middle of nowhere because they were Assassins and their enemies control the world.
The Scarlet Crusade in World of Warcraft is an entire faction of this, mixed with Knight Templar and Corrupt Church. They managed to survive and organize themselves to fight the Scourge, but are so paranoid that they attack on sight pretty much anybody who isn't them.
In a more meta example, many characters in RPG games that do not limit inventory too much often evolve into this, carrying/storing a substantial amount of weapons, armors, ammunition, performance boosters, spells etc. Just in case.
Achenar in the fourth Myst game acquires something of a Crazy Survivalist vibe, constructing elaborate Bamboo Technology security-measures to keep pesky animals from stealing his carefully-horded supplies.
Margaret in College Roomies from Hell!!! has been on a mission of preparing for the Apocalypse since she found out that Satan really exists. She has guns, bombs, and can kill wolves with her bare hands.
Many people who choose to play the game in Survival of the Fittest turn into this or already were at one point or another, including recent character Kathleen Martin. Interestingly, Kathleen is the way she is because her father is also a Crazy Survivalist.
Interestingly, the episode was something of a Deconstruction of the Survivalist stereotype. The Survivalist camp was peopled by disgruntled, angry people who were practically chomping at the bit for the day when things finally fall apart. When things actually do fall apart temporarily, due to a power outage at the nuclear plant, the Survivalists almost immediately start fighting amongst themselves for control over food and water supplies. Meanwhile back in town, people are finding it surprisingly easy to hold it together and get through the crisis, as if all of the disgruntled angry people who would have caused problems had already left...
To give a hint of Saxon's mindset, in the 1960s he was a member of George Lincoln Rockwell's American Nazi Party and Anton La Vey's Church of Satan, and wound up quitting both because neither was evil enough for him.
This trope is the reason why people who take emergency preparedness more seriously than most call themselves "Preppers" instead. The "Crazy" part is averted by at least one notable survivalist/prepper blogger, who advises to share your stocks with less-than-prepared people as soon as your own well-being is secured.
An article once actually argued stating that in the case of actual total societal collapse, these kind of people will be the first to go. Turns out the most important thing After the End will still be the ability to form social connections. (although other important skills include digging wells, brewing booze (seriously), growing crops and building shelter or something)