Immortal Assassin

Someone's put the hit out on you. But no matter, you're armed and dangerous yourself, and when the hitman catches up with you, you get the drop on him, and simply put two in his chest. Problem solved, crisis averted.

And then he gets up, dusts himself off, mutters some kind of pithy one-liner, and comes after you again.

You've just run into the Immortal Assassin.

This character shows up frequently in works of fantasy and science fiction, as well as comic books. The professional killer who themselves cannot be killed. Either they are straight-out indestructible, or they possess a Healing Factor that lets them recover from any injury. Why they hire themselves out as hitmen vary from character to character.

Depending on the universe, the Immortal Assassin may have been given their immortality through supernatural or technological means. Often, Immortal Assassins are much older than they appear, not able to die of natural causes, and as such can have a bad case of "immortal angst." If they hail from a time and place before gunpowder was invented, they may prefer bladed weapons or hand-to-hand combat, eschewing guns as "uncivilized" or "clumsy." As a consequence, they will possess phenomenal martial arts skills, honed from hundreds of years of practice.

Many Immortal Assassins consider themselves absolute professionals, devoted to the job at hand. They see killing as an art form, and make a serious effort to be as close to perfect as they can get. They may adhere to their own version of a "warrior's code," with a strong sense of personal honor. Often, this is because they come from ancient cultures that put a great emphasis on honor and martial prowess, and they see their careers as an extension of that.

Of course, there are exceptions. Some Immortal Assassins are sadists who kill out of pleasure or out of boredom. Being unable to die has left them so emotionally detached from the human race that killing mortals is little more than a game to them, a way to pass the time. Others are simply in it for the money. And then, some are just Ax Crazy...

Most of the time, the Immortal Assassin is the villain of the story. They can be a Knight of Cerebus, brought in by the Big Bad when all other plans have failed, a genuine unstoppable Badass more dangerous than any our heroes have yet faced. Or a Diabolus Ex Nihilo, particularly if they're so unstoppable that making them a regular character would ruin the drama. Alternatively, they may be a sympathetic character, particularly if whatever circumstances led to their becoming immortal or an assassin (or both) are tragic enough. On occasion, they will even do a Heel Face Turn, join the heroes, and become The Atoner, although that may not last. If part of an ensemble, they may even be used for comic relief: since Immortal Life Is Cheap, the Immortal Assassin can suffer truly horrific injuries and shrug them off.

There may be ways in-universe to defeat the Immortal Assassin. The Assassin may have a carefully-guarded weak spot, or they may be injured so greviously that their healing factor simply may not be able to compensate. Another option is total physical destruction of the Assassin's body, so that there is nothing left for the healing factor to regenerate. Use of Applied Phlebotinum may kill them, or deprive them of their immortality. Alternatively, the Assassin may be neutralized without being killed, imprisoned somehow, or even become Sealed Evil in a Can. Or in some cases, if the Assassin is just in it for the money and has no personal stake in the proceedings, simply calling off the hit will be enough.

There may be overlap with the Implacable Man, particularly if the Immortal Assassin isn't entirely human.

Anime and Manga

 * In Mnemosyne, an assassin keeps trying to kill Rin, and keeps coming back, no matter how many times she herself gets shot, stabbed, and blown up. Fortunately, Rin herself is immortal too.
 * Kakuzu of Naruto isn't quite immortal, but needs to be killed five times in one battle before he actually dies. He's also one of the oldest living characters; he was exiled from Taki for failing to kill the First Hokage, however many years ago that was.

Comic Books

 * Deadpool
 * The Saint of Killers from Preacher (Comic Book).
 * The Kindly Ones from The Sandman, although they can only be called upon to punish a kinslayer.

Fan Fiction

 * The focus of the Ranma ½ story Relentless, though the killer is a demon (or even Eldritch Abomination) known as the Reikoku, sent to perform an assassination, rather than a normal assassin who happens to be immortal. Its weaknesses: it takes a day to come back to life, and if a single person can kill it three times, it will be banished back to its home dimension. Unfortunately, each time it comes back to life, it will have developed an impenetrable defense against any attacks used against it the previous time, plus it will have developed brand new attacks, including tailor-made Flaw Exploitation attacks. It might seem like a good idea to destroy its corpse, but that just brings it back to life instantly. Oh, and if any of your friends attack it in order to help you, they get added to its hit list. And three total kills amongst you and all your friends aren't enough to finish it, it has to be three kills by the same person. Have fun!

Film

 * Many characters in the Highlander universe have made their living being Immortal Assassins, but most notably the Kurgan from the original film. He hires himself out to Clan Fraser in their battle against Clan Macleod, in exchange for the privilege of killing Connor Macleod himself.
 * Most Terminators are specifically designed to be unkillable killers; the only way to make the T-800 in Terminator 2 seem vulnerable was to create an even deadlier Terminator: the T-1000.

Literature

 * The Gholam of Robert Jordan's Wheel of Time is basically an Anti-Magic T-1000 designed to assassinate magic users--so terrifying that only a handful were ever made. Only (and probably starvation) can possibly do any damage, and that's not really a practical solution.
 * Ghost, of R.A. Salvatore's Cleric Quintet series, was a relative weakling who used a magic artifact to switch bodies, kill the target who is now in his weak body, and then heal it again using a magic ring of regeneration.
 * James Spector, AKA "Demise," from the Wild Cards series. Originally killed by the Wild Card virus, he was resurrected with an experimental cure. He gained both a powerful healing factor and the ability to "project" his agonizing death onto anyone he chose, essentially killing them with a thought. He was decapitated when a political assassination went wrong, and his body was destroyed by cremation when it became clear that he was trying to GROW A NEW HEAD.
 * The Night Angel from the Night Angel trilogy by Brent Weeks. He/she/it is literally immortal assassin although the immortality comes at a terrible prize: . Cue a whole lot of immortal angst and be done with it.
 * The Mercenary from The Bartimaeus Trilogy, while not strictly immortal, is incredibly resilient. Through his huge Healing Factor and resilience to magic, he survived a long fall from a cliff, survived being smashed under a huge rock and survived magic that could destroy demons, let alone humans. Unlike most examples, he is not the main villain.

Mythology

 * Achilles. Made unkillable when his sea-nymph mother dipped him in the River Styx. Except for the heel by which his mother held him, but hey, what are the odds of that ever being a problem?
 * The heel is a much later Roman addition to the myth. In the Iliad, he didn't have the heel issue, because he was just that good.

Television

 * The television show Lexx has an immortal assassin, Kai, as one of its main characters. He literally is unkillable and one of the subplots is him finding a way to die.
 * Warehouse 13 features Marcus Diamond, The Dragon to Season 3's Big Bad. Technically he can't be killed because
 * The Highlander series featured several. Christoph Kuyler claimed to be the most prolific assassin in history, as well as the less theatrical Anthony Galen and Kamir, the last of the thuggee assassins.

Video Games

 * From the point of view of the enemies, ANY player character is one of these. Even if they manage to kill you, you just resurrect at the nearest save point and keep on coming. A few examples below are justified since their means of resurrection are actually addressed within the narrative of the game:
 * Raziel from the Legacy of Kain series. Killed and resurrected twice already before the events of Soul Reaver, by the time the player meets him he is a soul-devouring revenant animated by an Eldritch Abomination for the sole purpose of bringing down Kain and his empire. His physical body is essentially a half-rotted corpse, without skin, internal organs, or even a lower jaw. And if this body takes too much damage, he simply shifts to the spectral plane until he builds up enough life energy to return. And since time stops on the material plain when this happens, from anyone else's perspective he just pops out of existence and then immediately back in again at full strength. The Elder God specifically says he is "beyond death." He can't be killed because there is simply nothing left of him that's killable.
 * Jack and Subject Delta from the BioShock (series) series: functionally immortal because the game's equivalent of save points - the Vita-Chambers - are coded to their specific DNA. No one else in Rapture can use them,

Web Original

 * The eponymous bad guy from The Horribly Slow Murderer With the Extremely Inefficient Weapon.