Suicide for Others' Happiness

This is essentially I Want My Beloved to Be Happy but in this case a character wants to erase themselves from existence/kill themselves because they think that it will make the one they love/care about happy.

Heroic Sacrifice is when a character trades their life for something they honestly and reasonably believe is clearly worth more than therir life, such as the lives of two people or to spare another a Fate Worse Than Death. In other words, the decision is based on valuing the lives of others over their own. This is when a character kills themselves or deliberately does something likely to result in their death because they believe others will be happier with them out of the picture. They're valuing the happiness of others over their own life.

For example, if we put our characters onboard the Nostromo in Alien, and Bob attacks the alien, knowing he'll probably be killed but it will give Alice and Carl a chance to escape, that's Heroic Sacrifice. If he then discovers the alien has been killed by a falling piece of equipment, but decides not to rejoin Alice and Carl because he knows Alice will be happier married to Carl than him, even though he knows the escape pod is his best hope at survival, it's this.

Compare It's a Wonderful Plot, where (as a Shout-Out to It's a Wonderful Life), a character gets to see what would have happened if they had never existed. As such plots usually prove, this sort of thing rarely makes anyone nearly as happy as the person doing it thinks it will.

Compare/Contrast Driven to Suicide or Undying Loyalty.

Truth in Television unfortunately and let's just leave it at that.

As a Death Trope, Spoilers ahead may be unmarked. Beware.

Examples of Suicide for Others' Happiness include:

Anime and Manga

In Code Geass, something like this happens when Lelouch plans a Zero-Approval Gambit, all so that the hate of the world will be focused on him and hopefully die with him, leaving his sister Nunnally a better world. As he dies, Nunnally tells him she would rather have remained with him in exile.
In Pandora Hearts Vincent is so obsessed with his older brother Gilbert that he wants to do this in regards to him.
Happens in Kannazuki no Miko: Chikane plans to die and be erased from Himeko's memories in order for Himeko to live on and be happy. It doesn't really work out, because even without her memories, Himeko's love for her remains ingrained into her very being, causing her anguish. So Chikane comes back from the dead for her.
Fairy Tail: After realizing the pain she caused Meredy, Ultear tries to kill herself to atone. Despite Meredy's anger, she forgives Ultear and prevents it.
Mirai Nikki: Yuno eventually goes this direction in regards to her love for Yukiteru.
In Nabari no Ou Gau is so devoted to Raikou that he is willing to kill himself to make Raikou happier.
In Bleach Shishigawara is utterly devoted to Tsukishima and is willing to throw away his life for him. The implication being that he would do so if it would help Tsukishima in his plans and make him happier in the long run.
In Katekyo Hitman Reborn Gokudera is implied to have a crush on Tsuna and was prepared to sacrifice himself for Tsuna's happiness during the battle with Belphegor but stops when Tsuna tells him he wouldn't be happy if he sacrificed himself.
In Monster Johan's whole "perfect suicide" plot was an attempt to eradicate his own existence in order to make his sister Anna happy. As Anna puts it, this "suicide" was the "only expression of love" that Johan could convey.
Serial Experiments Lain: Lain once gives Alice a confession of love. The anime ends with Lain deleting herself from existence for Alice's peace of mind, arranging things so that she can marry her high school crush, and spending eternity watching over her from the Wired.

Film

In the James Bond film The World Is Not Enough, the Big Bad (or possibly The Dragon, it's not made clear) is willing to die in order to further Electra's plan to irradiate all her competitors' oil by blowing up a nuclear submarine. The fact he's slowly dying from a bullet wound to the head probably helps though.
Donnie Darko: Donnie allows himself to be killed by the falling plane turbine to allow the various people in his life to live/be happy.
The Butterfly Effect: One of the endings has Evan Treborn go back in time to strangle himself with his own umbilical cord while still in the womb, resulting in a stillbirth (and the fairly creepy implication that his mother's previous miscarriages were the result of something similar). The people Evan cares about, for whose sake he does this, do in fact go on to lead better and happier lives.
In the 1996 movie Kissed, a young man falls in love with a seriously disturbed girl. She has been attracted to dead things since childhood, and took a job in a mortuary to give herself access to comely dead men. The young man tries to lead her into a (marginally) healthier relationship with him, and the girl tries, but is revolted by sex with the living. The young man eventually commits suicide in front of her so that she will finally love (and make love) with him.
The alcoholic main character in A Star Is Born kills himself so his wife won't have to sacrifice her career to care for him.

Comic Books

Sin City: Poor John Hartigan. He went to incredibly great lengths to protect Nancy Callahan from those vicious Complete Monsters calling themselves the Roarks. He killed Roark Junior AKA That Yellow Bastard to save Nancy's life. Before that, he let himself be Blackmailed by Senator Roark to protect Nancy and his family from the Senator's wrath. He sent Nancy away, promising to expose the Roarks and clear his name. However, once he was alone, he killed himself, believing Nancy will be safe from the Senator's wrath this way.

Literature

In Twilight, Jacob threatens to do this, but Edward says it's just a ploy to get Bella to kiss him.
The Night Circus: because The Challenge only ends when one of the competitors kills themselves, and The Challenge is an intimiate experience which inevitably results in the two competitors loving one another, both challengers go through a period where they contemplate suicide to relieve the other from continuing the game.
In Death of a Salesman Willy Loman kills himself (by having an "accident" in his car) so his wife and sons will get his insurance money.
Sacred Sins by Nora Roberts: Joey is a troubled teenaged boy who is depressed, suicidal, and has dabbled in alcohol and the occult as attempts to cope with his depression, stemming from his mother's divorce from his alcoholic father and the fact that his father apparently doesn't want anything to do with him. His mother has remarried, the stepfather is basically the opposite of Joey's father, and the two of them have a baby. So on Thanksgiving night, after dinner, he sneaks out of the house, goes to a bridge, and jumps off it, convinced that his mother and stepfather will be happier without him and that they have the baby who can just replace him. He dies in a hospital, leaving his mother, stepfather, and the psychiatrist who tried to help him in tears.

Western Animation

In a Tom and Jerry short, a duckling thinks Tom is his mother, so Tom takes the opportunity to try and eat him. Eventually the duckling figures it out, and so decides that "if eating me will make my mama happy, then go ahead." It is then that Tom has a change of heart.

Video Games

Mother 3: In the final boss fight, Claus, Lucas's brother, finally comes to his senses. Then he fires an attack that he knows will be deflected back at him and kill him. He apparently did it because he thought his family would be happier without him, and that he should be with his dead mother.