"Some pirates achieved immortality by great deeds of cruelty or derring-do. Some achieved immortality by amassing great wealth. But the captain had long ago decided that he would, on the whole, prefer to achieve immortality by not dying."
― Terry Pratchett, The Color of Magic
"Surely God would not have created such a being as man, with an ability to grasp the infinite, to exist only for a day! No, no, man was made for immortality."
Users possess an infinite life span, as they can never die, never age, and can shrug off virtually any kind of physical damage. Some users are the defensive type, simply preventing all damages, to appear physically invulnerable, while others are the regenerative type, surviving and quickly recovering from anything you throw at them while at the same time they are capable of resurrecting themselves instantly after death and completely self-sustaining, free from all bodily necessities.
Some may only possess the power of:
Death: No body to destroy. The soul, one that is not of a physical being, does not inherit physical characteristics, such as concepts of destruction, therefore cannot be destroyed; in short, the user cannot die because it is already dead. Most common form of immortality.
Cannot overcome the End of Time, unless the form of immortality is an absolute type, hence why just like Regenerative Healing Factor, it is unclear how long it would last.
May be erased from history via the effects of time-manipulating powers, killing the immortals in question before they become immortal.
While users are immune to the ravages of time, most are vulnerable against direct application used against them.
Nonexistence may wipe the user out of existence, as opposed to simply killing them biologically.
May have certain weaknesses that are lethal (i.e. decapitation, disintegration, poison).
May have weaknesses to single source (item, event, person, etc.) that is lethal to them.
May be killable by certain specific way, item or people.
User may go mad, from the effects of time and boredom.
This can also cause madness overtime because the immortal is forced to watch those who aren't immortal die.
May forget events that happened long ago.
Some immortals could be infertile, or they're incapable of passing this ability to their descendents.
Immortality may depend on outside sources and objects (i.e. Horcruxes, Shikon shards).
Can be sealed in an empty dimension with no chance to escape.
It is highly likely that various kinds of Immortality can become a curse because whoever is close to them or even their friends had died, the user would be left behind, unless the user is also gifted the ability to teleport to both Earth and Heaven, or alternatively Meta Teleportation to keep the curse of being immortal at bay.
Teitoku Kakine (A Certain Magical Index) achieved a form of immortality by creating a human tissues (and a new body) out of his Dark Matter.
Ladylee (A Certain Magical Index) is an immortal, in that when she grew weary of living, she sought to use powerful magic to kill her, which did not work.
Tenzen Yakushiji (Basilisk) having his symbiote "eat" away his wounds and restoring any ravages of time or battle, even reattaching his head by sealing the cut.
Creed Diskenth (Black Cat) possesses the God's Breath nano-machines within his body, regenerating even fatal wounds in seconds and maintaining his youth, thus granting him immortality aside from any brain damage being irreparable.
Sōsuke Aizen (Bleach) gained immortality after fusing with the Hōgyoku.
The Truth (Fullmetal Alchemist) is invincible, immortal and invulnerable.
Utsuro (Gintama) possesses immortality by harnessing the Altana energy of Earth to prevent aging and recover from wounds and diseases.
Kouka (Gintama) possessed immortality by harnessing the Altana energy of Kouan to prevent aging and recover from wounds and diseases. However, when she left the planet for good, she weakened overtime and died.
China (Hetalia) is the only nation stated to be truly immortal.
Yūta (Mermaid Saga) is a 500 years old immortal since unwittingly eating mermaid's flesh.
Mana (Mermaid Saga) is a 15 years old immortal since being fed mermaid's flesh.
Masato (Mermaid Saga) is an 800 years old immortal since eating mermaid's flesh.
Ban (Nanatsu no Taizai) acquired immortality after drinking the Fountain of Youth.
Meliodas (Nanatsu no Taizai) was cursed with the immortality by the Demon King.
Orochimaru (Naruto) considers himself immortal with his Living Corpse Reincarnation to transfer his soul to another body and his Cursed Seals as anchors of his conscious.
Hidan's (Naruto) main advantage is his inability to die by physical damage, though he is vulnerable to death by lack of nutrient.
Kakuzu (Naruto) attained a form of immortality (though he denies to think of it as such) by tearing hearts out of others and integrating them into himself, extending his lifespan. He kept five inside him at all times.
Madara Uchiha (Naruto) claims he has achieved complete immortality due to hosting the Shinju, as he regenerated form his torso being blown apart. Only when the tailed beasts were all pulled out of him did he die.
Kaguya Ōtsutsuki (Naruto) is immortal, in that she has tremendous regenerative powers, and that the only way to defeat her is to seal her person away by splitting her chakra into the nine tailed beasts.
Gemma Himuro (Ninja Scroll) putting his severed body parts back together, even his head is possible, rendering him immortal.
Due to her race, Jibril (No Game No Life) has age 6407 years old, she has incredibly vast knowledge and high magical abilities, in two words; she live with gathering many old and new knowledge, in other words; she can no longer age or die.
Yume Hasegawa (Pupa) is an immortal monster incarnated into human form, possessing regenerative abilities that rendered her very difficult to kill.
Utsutsu Hasegawa (Pupa) has been fed the flesh of her immortal "sister", giving him tremendous regenerative powers that made him more or less immortal.
Rin Asogi (RIN ~Daughters of Mnemosyne~) is immortal, due to a magic spore from Yggdrasil. she can even handle more alcohol than a normal person.
Free (Soul Eater) is a werewolf from the Immortal Clan, and therefore, immortal. He can only be harmed and killed by the "Witch-Hunt".
Kojō Akatsuki (Strike the Blood) is revealed to be immortal, even by vampire standards after regenerating from complete decapitation.
Tōta Konoe (UQ Holder) cannot regrow limbs unless they are completely destroyed, but otherwise is immortal and can reattach any of it, including his head.
Karin Yūki (UQ Holder) has one of the highest ranked forms of immortality, stating that she's "not permitted to get hurt or die"
Elder Toguro (Yu Yu Hakusho) stated that his regenerative powers enables him from dying. This prevented him from dying from Kurama's torturous Sinning Tree.
Notorious B.I.G. (Jojo's Bizarre Adventure) is an immortal stand due to it's Reforming powers and the fact it activated through the death of its original user, and as such, the original user cannot be killed in order to be rid of it.
Through the unknown power of his Stand, Nijimura's Father (Jojo's Bizarre Adventure) is effectively immortal and possesses extraordinary healing capabilities.
Porky Minch (Earthbound) has abused Time Travel so much that his body is stuck in the current timeline and cannot age nor die.
It is believed that Ganondorf (The Legend of Zelda) is immortal due to the Triforce of Power.
Clockwerk (Sly Cooper) has kept himself alive for millennia thanks to his cybernetic body and his jealousy and hatred of the Cooper Clan.
The Darkness (Skylanders) can only be killed by the Core of Light.
Solaris (Sonic the Hedgehog) is a super-dimensional life form and the Sun God of Solenna, and exists in all timelines that he is immortal unless he is killed simultaneously in every temporal point.
Presea Combatir (Tales of Symphonia) is immortal and invulnerable because of a combination of her exsphere and her special ability Suppress
Kaguya Houraisan (Touhou Project) drank the Hourai Elixir, which grants her immortal in every sense of the word: she does not age, is immune to disease, and can regenerate from even being completely disintegrated.
Though he can be imprisoned and sealed away, Grima (Fire Emblem) can only be truly and permanently killed by his own hand.
Snow White (Valkyrie Crusade) is a immortal princess that is always trying to die, but nothing works.
Lord Voldemort (Harry Potter) acquired immortality by splitting his soul and hiding the fragments in various objects as anchors, though when his body was destroyed, he existed as a spectral form that many others would prefer death over.
Fawkes (Harry Potter) is a phoenix, who will be reborn with all of his memories intact upon death, and thus immortal, being the only known creatures in the wizarding world to have natural immortality.
Adam Monroe (Heroes) possessed immortality due to his tremendously advanced regeneration ability, though once the ability is taken away from him, he died within seconds.
Nathan Young (MisFits) is immortal.
Starscream (Transformers G1) possesses an immortal Spark, soul energy, meaning even if his physical vessel is destroyed he will live on.
Jason Voorhees (Friday the 13th) can only be truly and permanently killed by his own family members.
The Beast (Doctor Who) claims to have existed before our universe was created
Candyman (Candyman) has lived for centuries
Ashildr AKA Me (Doctor Who) is effectively immortal due to being given a Mire computer chip.