Immortality is the term given to people who won't die naturally. Immortality is a common power in fiction featuring supernatural beings such as Gods, werewolves, vampires etc. Others can be gifted with it via mutation, cosmic powers etc. There are several variations of immortality with various ranges of usefulness:
Longevity is the power to live a long time. People gifted with this type of immortality cannot die from natural causes, old age, illnesses etc, but can be killed by unnatural causes.
Examples include Kakuzu from Naruto, Odin from Marvel Comics, Shadow the Hedgehog from Sonic the Hedgehog
2: Immortality without regeneration
This type of immortality is not useful for combat. Essentially bodily harm cannot kill you but your original form can be mutilated. An immortal of this category can be maimed and rendered useless in battle. If the character in question has high durability then this type of immortality can be more useful.
Example: Voldemort from Harry Potter, Vincent Valentine from Final Fantasy, Hidan from Naruto.
3: Immortality via regeneration
You can maim the person, kill him etc and he'll still come back. This type of immortality hinges on how well the character can regenerate. Most high tier regeneration grants immortality.
Example: Reload from Biomega, Alucard from Hellsing, Dark Schneider from Bastard!!, and Wolverine from Marvel Comics.
4: Immortality via Godhood or protection from a deity
This kind of immortality is granted by a God or is given by virtue of Godhood. Only a God of higher status can override it.
Example: Juggernaut from Marvel Comics, Lucifer Morningstar from DC/Vertigo Comics.
5: Perfect Immortality
Characters who exist unbound by conventional life or death, or do not exist at all, and thus cannot be traditionally killed. Typically, abilities such as erasing the target's existence or "killing" them on higher levels of existence are needed to destroy them.
Example: The One Above All from Marvel Comics, The Presence from DC/Vertigo Comics, Kami Tenchi from Tenchi Muyo!
The person attains a sort of immortality by bodyhopping, transferring their soul to another body.
Example: Orochimaru from Naruto, Violator from Image Comics, Darth Sidious from Star Wars (Legends), and Dante from Fullmetal Alchemist's first anime.
Self explanatory. The undead generally double up with other types of immortality. Zombies may possess similar resistances to the "Immortality Only" category. Ghosts occasionally double up with "Perfect Immortality" as they can not usually be killed again.
Example: Ghosts and Inferi in Harry Potter, Jason Voorhees from Friday the 13th.