In many works, as in Real Life, Rape Is a Special Kind of Evil, an appalling crime that brutalizes the victim and can destroy lives, or worse. While some other works play rape for sexual fantasies or laughs, these treat it soberly, for a dramatic purpose.
That doesn't necessarily mean that it's treated tactfully. All too often, it's a case of the Disposable Woman becoming the Damsel in Distress (or even getting Stuffed Into the Fridge) to motivate the male vigilante. If multiple rapists were involved, expect the vigilante (or, occasionally, the victim) to go on a full-bore Roaring Rampage of Revenge. Male examples, outside of the Boys Love, are rarely played for drama.
It is also used to make an otherwise unapproachable woman or man into a needy one. Like Rape Is Love... except someone else provided the rape. It is also used to motivate an overly independent or promiscuous bad girl or bad boy to change his or her ways.
Horrifically overused in Fanfic, for a number of reasons. Most often, it's just as a cheap shock in backstory without bothering to explain it any further than a sentence. Sometimes it's used in a case of Die for Our Ship, in which the character the writer hates is the rapist, and the rape is used as a device to get the two desired characters together (usually after the character the writer wants to "win" the ship war kills the perpetrator). Sometimes it's just used to make a Woobie out of the writer's desired Canon Sue, or to pair the author's Mary Sue or Marty Stu with the victim in a Hurt/Comfort Fic. It's arguable that less than 1% of Fanfic actually uses Rape as Drama effectively, as most of the 10% of "good fics" that Sturgeon's Law claims there to exist avoid using rape entirely. When in a story the handling of rape amounts to a mention of having happened in the backstory or depicting the act and then neglecting to explore the effects on the victim, thus completely failing in make an impact on the reader, it becomes an example of Rape Is the New Dead Parents.
Like Blackmail, to list all the variations and permutations of Rape as Drama here would probably be an exercise in madness.
No real life examples, please; First, this is a rape trope, and All The Tropes does not care to squick its readers. Second, Real Life is not a Drama. Fictional examples should be listed on the related pages listed in the article.