Basic Trope: Immortality is achieved through ethically dubious methods and/or is inherently evil.
Alice can live forever... at price of killing people by draining their life forces.
An immortal always becomes insane.
Even attempts to simply increase life span are evil and must be stopped, even when God or another benign being is responsible.
Based on the idea that the ideal life-time isn't longer than natural, people figure it's almost definitely shorter (it's not going to happen to be exactly the same), and have everyone killed at 50.
Bob, while immortal, is definitely not evil, but he is a big jerk.
Alice has extended her lifespan by a few decades using a highly controversial medical procedure.
When someones lives too long, it upsets the balance of life and death, and the laws of magic and destiny cause death and pain in the world to bring back the balance, but the only true solution is the death of the immortal.
An immortal always will become insane because their long lifespan means that they will experience more loss and tragedies.
Immortals quickly become reckless since they can no longer be killed, whether it be by accident or capital punishment.
Inverted: Not only is immortality is acceptable and desirable, but any willingness to or acceptance of death is considered suicidal and immoral.
Immortality is possible only by becoming an exceptionally good.
Parodied: Bob has found a safe and responsible way to make himself immortal without any damage or ill effect to himself or anything around, then is subjected to an panicked mob out to at least try to kill him when he goes public with his secret.
The show flip-flops between its portrayals of immortality. Sometimes it requires immoral actions to be sustained, sometimes it's harmless and the immortal is a perfectly decent person.
Turns out the child was evil.
Immortality never has any moral stigma attached to it.
The villian's reasons for being evil have nothing to do with immortality.
"The executives think that immortality is evil, looks like we'll have to portray it as such."
"An immortal having no problem with his condition seems boring and might step into Mary Sue territory."
Lampshaded: "Why does being immortal always require people to eat souls and whatnot? Can't they find a way that's harmless?"
Invoked: Emperor Evulz deliberately puts a "must eat souls" factor into his immortality treatment so that it will corrupt anyone who steals the secret.
Exploited: The Big Bad offers Alice an immortality potion, knowing that its side-effects include puppy-chewing evil, because he wants her on his side.
Defied: In the middle of Alice's rant about his "evil" nature, the vampire Bob argues that he can live from artificial blood and could still be a productive member for the society at night.
Discussed: "I bet that guy's evil — immortals always are!"
Conversed: "Why is it that immortals in these stories are always portrayed as insane monsters?"
Deconstructed: When someone tries to argue that Vampire Alice would need to kill people to drink blood, the kind hearted vampire tells that she can just feed of animals.
Reconstructed: Although most of the people who attempt that can't consistently resist the desire to drink human blood.
Played For Laughs:
Bob's immortality gives him the gall to go to the same bar every day for hundreds of years just to gloat about how all the other regulars from generation to generation are "looking a bit older, and a bit deader". He is regarded as a legendary Jerkass amongst the townsfolk, who warn The Hero not to venture to said bar, lest he come back either depressed or furious.
An immortal tells people that he's not evil because he lives for ever. He is for completely different reasons.
Played For Drama: Bob has the power of immortality due to winning the Super Power Lottery, and doesn't even need to suck souls to remain immortal. Sadly, there is a heavy prejudice against immortals, causing Bob to lose his wife, family, friends and everything that he held dear.