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 for 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 Fan Fic, 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 Fan Fic actually uses this trope effectively, as most of the 10% of "good fics" that Sturgeon's Law claims there to be avoid using rape entirely.
Like Blackmail, to list all the variations and permutations of this trope here would probably be an exercise in madness.
See also Attempted Rape, Prison Rape and Rape as Backstory. Contrast Black Comedy Rape for when it's Played for Laughs and Got Over Rape Instantly when the rape is ignored and the victim immediately shows romantic or sexual interest.