Decapitation Required

"Victor: Tell me something, Jimmy. Do you even know how to kill me?

Logan: I'm gonna cut your goddamned head off. See if that works."

- X-Men Origins: Wolverine

When a character or group is lauded to be immortal, indestructible, or otherwise unkillable, oftentimes one of the few if not the only things they are not immune to is decapitation. This could be a reveal, it could be known from the getgo as "the only way to kill them"; or, as in the quote above, it could be in-universe speculation which may or may not get put to the test.

The reason for the prevalence of this trope, particularly of the latter form, probably has its roots in the Rule of Perception. An audience can swallow a character being shot full of bullets or losing a gallon of blood and shrugging it off, even when there isn't a good reason for it. And the removal of vital organs, up to and including the heart, is still conceivably survivable because hey, they can just grow a new one! After all, one can survive a few seconds with no heart even in real life, so as long as you can regenerate within that timespan you're good, right? But decapitation crosses the line from "should be dying" to "already dead by definition," and you have zero time to heal. In the minds of viewers and characters alike, you just can't be alive if your head is not attached to your neck, and it takes more than a Healing Factor to explain how you can be.

Removing the Head Or Destroying The Brain is a specific subtrope for undead. That said, in general beings who are "already dead" have a higher chance of averting this trope than those who aren't. And don't even bother trying this on Dem Bones, unless your aim is comedy.

The intersection of Achilles Heel with Off With His Head. When this applies to a robot, it's likely because of a Cranial Processing Unit. When cutting something's head off doesn't kill it, it's Losing Your Head. See also Chunky Salsa Rule and Boom! Headshot!.

Anime and Manga:

 * In The Twelve Kingdoms beheading is one of the certain ways to kill an immortal (the others being cutting the body in two and use of special enchanted weapons), and is shown to be the preferred method in execution.
 * Subverted hard with Hidan from Naruto. Azuma thinks it'll work and succeeds, but all it does is piss Hidan off.
 * Averted in Ninja Scroll: Jubei thought Gemma was dead from this, but he reappears with a faint scar around his neck.
 * Berserk has Guts fighting a monster that can regenerate as long as its head is intact...which it brags about to Guts.
 * Mermaid Saga. Not the only way to kill an immortal, but the most effective and most attempted.

Comic Books

 * In the French series Zorn and Dirna, Death is trappped in a magical mirror, and now every single living creature is fated to age forever, unless the spinal column is severed, in which case the dead one's soul goes into the killer's. It is specifically mentioned that butchers have adapted by developping the skill of removing meat from an animal without cutting the spine.

Film:

 * In the Highlander series, beheading is the only thing that will kill an immortal. The best way to behead an immortal is with some variety of blade, hence all the Sword Fights that immortals get into in the series.
 * The Mummy Returns: The only way to kill an Anubis Warrior is by cutting off its head.
 * In addition to the page quote, X Men Origins Wolverine uses this This is shown in the movie as being the only way to kill anyone with a Healing Factor.
 * Horribly subverted in The Thing.

Folklore:

 * A specific remedy for vampires.
 * In fact, it's a very popular folkloric cure for practically any kind of monster and, as a sort of bonus, works just as well on humans.
 * Zombies in general, with the exceptions of Braindead and Return of the Living Dead.
 * Averted with the Hydra from Greek Mythology. It started off with nine heads, and every time one was cut off it would grow two in its place. Hercules finally defeated it by cutting off its heads and having a friend cauterize the stumps with fire to prevent them from regrowing.
 * The weakness of Medusa, the gorgon. While her two sisters were immortal, Medusa had a mortal neck covered in metallic scales which could be severed, killing her.

Literature:

 * Played with in Mistborn. The Lord Ruler is lauded as an immortal god, and it's common knowledge that "decapitation only irritates him," so nobody ever tries this. It's also one of the many things he claims to have survived in a Badass Boast while fighting the heroes. However,, and according to Word of God it was a big fat lie.
 * In Brandon Sanderson's earlier work, Elantris, Elantrians are most reliably killed by beheading. Anything less will simply leave an unhealing, eternally-hurting wound. Burning also works.
 * The short story Dragon Reserve, Home Eight by Diana Wynne Jones features "hegs," people with superhuman abilities including being able to "mind read, kindle fire or more objects at a distance, heal or kill by use of mind alone, survive shooting, drowning, or suffocation..." By law, once discovered they are executed by beheading, which is the only thing they cannot survive.
 * In the Keys to The Kingdom series, beheading is one of the few ways to surely kill Denizens.
 * Played for Laughs in Terry Pratchett's Carpe Jugulum, in which vampires from different areas of uberwald have to be dispatched in varying ways (lemon in the mouth, nail through the knee, hide his sock) but all involve cutting off the head (which, conveniently, also works on people).
 * The Brollachian from Shadow Keep is a part ogre part octopus brute that feels no pain and can regenerate missing limbs and chunks of flesh. However, Maryld stated that he can be slain if beheaded, but the heroes never get the chance of trying this on it.

Live Action TV:

 * Heroes: It's stated that characters with a Healing Factor can't survive decapitation, although it's never actually shown. The more commonly referenced means of taking one down is by shooting or stabbing a very specific point in their brain, but that only works temporarily; if the object is removed, they will still heal. Not so, allegedly, for full decapitation.
 * On Supernatural, this is how the "unkillable" Leviathans are finally defeated. It still doesn't actually kill them but it incapacitates them until their heads crawl back over to their bodies, a problem solved by simply putting the head in a box.
 * It seems that in this case, removing the head doesn't work, but destroying the brain does.
 * Subverted In Torchwood Miracle Day. Jack Harkness suggested cutting off the head of an assassin who is being kept alive by the miracle (despite being burned to a crisp. The authorities try it, and he's still alive. Jack himself also subverts this in all post 9th doctor appearances except the aforementioned Miracle day.
 * "Braining" always worked on Star Trek the Original Series.
 * Decapitation is one of the few ways to kill a vampire in Buffy. They instantly turn to dust once their head isn't attached to their body. Angel brings up another caveat; vampires have a Healing Factor but their brain won't heal from some injuries, meaning they could be left brain-damaged for all eternity if something happened to it. This is mentioned, but it never comes up in the actual story.

Tabletop Games:

 * Subverted in DnD; Vorpal weapons instantly decapitate enemies on a critical hit, but some enemies either don't have heads to remove, or aren't inconvenienced by it.
 * Specifically, the latter includes monsters with regeneration (though Ogre Mages need to reattach their heads within ten minutes), most Constructs, and Undead (save for vampires).
 * Pathfinder has Vorpal weapons that are much likes the ones in Dungeons and Dragons. In addition, Pathfinder also introduces the Jabberwock creature, which has a particular fear of vorpal weapons; striking one cause it to become temporarily shaken.
 * Decapitating a Harrowed from Deadlands doesn't kill them. It reduces them to fully conscious but helpless heads.
 * In the French RPG Trinites it is usually the surest ways to kill the eponymous beings for good.