Anime and Manga
In the Dragon Ball series, many antagonists seek the dragon balls to gain immortality including Vegeta, Nappa, and Freeza in the Dragon Ball Z series. Garlic Jr. achieves this feat.
In the anime/manga Naruto, five characters have shown the ability to find some way to increase longevity or become immortal, Sasori, Hidan, Kakuzu, Madara Uchiha and Orochimaru. Kakuzu is partially immortal because of his unique ability to add new organs (specifically hearts) to his body in order to increase his already long life though he doesn't view this ability as immortality. Orochimaru invented a jutsu through forbidden research which allows him to switch bodies with another person, allowing him to become partially immortal. Sasori turned his own body into a puppet and sealed his humanity in a small flesh and blood core, free from the human essentials forever. In contrast to Sasori, Orochimaru and Kakuzu, who had to find a special technique in order to increase their longevity, Hidan has the ability to never get injured by anything. Even the most grievous wounds could not kill him, and even decapitating him is more a nuisance than anything else. Hidan must periodically kill to retain immorality but since being buried alive, he is presumed to be died. Sasori, Kakuzu and Hidan are now all dead. Madara is considered immortal due to his seemingly endless chakra (physical/spiritual energy) supply. Tsunade has such powerful regeneration techniques that makes her practically immortal in battle.
Immortal Rain is a manga by Kaori Ozaki. The main character, Rain Jewlitt ( nicknamed Methuselah,) was cursed by his friend Yuca with immortality. He is a kind, gentle man who loves people, and 600 years of painful memories can be too much. He can't stand watching the people around him die and attempts to separate himself from human connections. But when a young bounty hunter follows him, she saves him from his loneliness, and he saves her from hers. Though it's not really mentioned, the tragedy is that the young girl, Machika, will become an old woman and die in the blink of an eye (or she'll be killed young); he will be alone again, with the memory of her death haunting him forever. That is, unless he can become a human mortal again. Though the world is jealous of Methuselah's immortality, he suffers from it and wants nothing more than to die.
In the anime Bleach, several of the series' races are very long-lived in some fashion, though not explicitly immortal. A race of humans called bounts are effectively immortal so long as they can find human souls to devour. They are born like any ordinary human, but when they are around 20–30 years old, they stop aging. Hollows are likewise very long-lived, and subsist of the same methods as the bount. Deceased human spirits, be they shinigami or simply ordinary souls, age at an extremely slowed rate, such that those well over 2000 years old will appear at most to be in their eighties. During the Arrancar Arc, the antagonist Szayel Aporro Granz attains immortality using his abilities of "impregnating" a victim with his DNA, then using their body as sustenance to recreate himself. The process could theoretically be repeated forever. Later in the series the main antagonist Sosuke Aizen obtains true immortality, but in the process he loses most of his power and is imprisoned for his crimes.
Naraku, the main antagonist of Inuyasha, became partially immortal when he rejected his human heart. He could not be killed unless his heart, which took the form of an infant called Akago, was destroyed. A good example of this is when Sesshomaru shreds Naraku to pieces (and yet he still survives) when they are fighting in the Netherworld, after Inuyasha destroys Naraku's barrier with Kongosoha (Diamond Shard Blast).
In Fullmetal Alchemist, immortality is partially achieved through the use of a Philosopher's Stone. By using energy stored in the stone (harvested from the lives of thousands of slain innocents), human souls can essentially leap from body to body (or, in some cases, inanimate objects), thus living on. However, doing so slowly destroys the soul until it can no longer support a new flesh-and-blood body, which quickly begins to rot as soon as it is taken over. Also, the main antagonists of the series, a set of homonculi, attain partial immortality. They are able to regenerate from otherwise deadly wounds multitudinous times before finally succumbing.
In Hellsing the Vampire Alucard (Dracula) has lived for 500 years. he hasn't died, but has been beaten twice. the first time was when he was killed as a human after a battle against the Ottoman Empire(he became a vampire by drinking the blood of his soldiers) the second time was when he was beaten by Abraham Van Hellsing.
In Code Geass, characters with the 'Code' have eternal longevity and immortality, and can grant the power of Geass to others. Once the Geass is fully developed, the Geass user can be granted the 'Code', the person who gave them the Geass has the choice to die after granting a person his or her 'Code.' Two characters with the 'Code', C.C. and V.V, are shown to have eternal youth and immortality. C.C. is immortal, neither suffering from age nor capable of being killed by conventional means. She has retained her prime physical form from the time she received the power of the 'Code', presumably sometime during the Middle Ages. She has also been shot fatally a number of times, been crushed by water pressure, burned at the stake, subjected to the guillotine, and placed in an iron maiden, all of which she recovered from. V.V. has also displayed the same longevity and immortality C.C. has, being able to remain 10 while his twin brother, Charles zi Britannia is 63. Charles has also forcefully taken away the 'Code' from his brother at one point in the series, gaining his immortality while V.V. died from fatal injuries. At the end of the series, C.C. became the last Immortal still having the Code after Lelouch erased his father, Charles from existence after turning the collective consciousness of humans on him. It is also speculated by fans that Lelouch forcefully took the 'Code' from his father at that point, having fulfilled all the requirements to possess it, and was activated after Lelouch died at the end of series, possibly making him an immortal, although the producers have confimed his death.
In the Slayers series, there have been a number of characters who appear to be immortal. In Slayers Next, it is revealed that a human who makes the Pledge with the Mazaku (Monster) race can gain immortality. A villain named Halcyform was able to achieve this by pledging with another villain named Seigram, who was indeed, a Mazaku.
In Death Note, if one uses the book, they can achieve partially immortality although still able to be murdered or killed by any means.
Read more about this topic: Immortality In Fiction