Medical Rape and Impregnate

A woman, probably someone who doesn't want children, is kidnapped, drugged, and forcibly impregnated by a Mad Doctor using someone's sperm, for all intents and purposes producing a Child by Rape. May lead to a Baby Factory situation. Definitely a Medical Horror.

Naturally, Good Girls Avoid Abortion, so this is a way to force a pregnancy onto someone. Possibly she will have a Convenient Miscarriage, but if the plot's usually gone this far to make her have a baby, she probably won't.

Someone that wants to perpetrate such an act is a Stalker with a Test Tube.

No real life examples, please; this is a rape trope, and All The Tropes does not care to squick its readers.

Examples of Medical Rape and Impregnate include:

Anime

Implied to have happened in Lyrical Nanoha, of all shows. Near the end of the third series, Big Bad Jail Scaglietti reveals that he impregnated his Quirky Miniboss Squad, the Numbers Cyborgs, with rapidly-growing clones of himself which he'd patterned his own mind into, ensuring that he could continue to wreak havoc across the multiverse even if the heroes arrested him. Whilst this appeared to be mostly consensual (though deeply squicky for a number of other reasons), it's worth remembering that the Numbers Cyborgs, at the time, included the kidnapped and brainwashed Ginga Nakajima, who would therefore also have been a candidate for this procedure. Happily, given the fact that this revelation ends up having no lasting consequences, it seems that Good Girls Avoid Abortion was quite strongly averted here.
- Supplementary materials state that this was a magical procedure, intended to implant upon Jail's death, and that since Jail was taken alive, no one was actually impregnated. Whew.
Almost happened to the titular character in Karin, since her condition as the non-vampire of her family actually was a consequences of being a spirit of psyche, a special type of vampire that can bestow fertility in other vampires. Therefore she's kidnapped and locked away by another vampire clan, who plans to do this to her.
Subverted in Ayashi no Ceres. Chidori goes through it when she's caught by the Mikages, but she ultimately dies before the embryo is implanted into her.

Comic Books

Elephantmen: This is how MAPPO creates its half-human Super Soldiers.

Fan Works

In the NCIS fanfic Laboring to Love a mad scientist kidnaps most of the team to perform such a procedure, except the team member left out of the kidnapping is Ziva. The mad scientist has been working on an artificial womb for men, and McGee is the test subject.

Literature

In Devil's Due, it's been determined by people who can see the future that a child between Lucia and Ben would be some kind of Chosen One. They try to blackmail Ben into seducing and impregnating Lucia. Ben is interested in Lucia, but is a gentleman and just can't bear to do it. So Lucia is infected with anthrax, kidnapped, and impregnated with Ben's sperm to do the job. The two agree to keep the child, even if they aren't thrilled with the circumstances of the conception.
Demon Seed by Dean Koontz has this happen, and the perpetrator is an artificial intelligence who calls himself Prometheus. He just wants to help humanity get rid of all its pain and misery and disease and male pattern baldness and of course, to live a life of the flesh by transplanting his consciousness into the child once it is born. It should also be mentioned that this child is not entirely human.
In The Merchant Princes Series, Miriam/Helge is forcibly impregnated by the Mad Doctor with her fiance's sperm (her fiance is in no way able to perform sex, it's an Arranged Marriage as is). She agrees to keep the child for political reasons, but eventually has a (semi) Convenient Miscarriage.
In Jason X: Planet of the Beast, a drugged woman is impregnated with Jason's... genetic material.

Live Action TV

This plays a major role in the Myth Arc of The X-Files, although the X-Files version involves extraterrestrial DNA instead of somebody's sperm. It's strongly implied to have happened to Scully during her abduction. Mulder even calls some of the conspirators "medical rapists" at one point.
An episode of Criminal Minds had a couple who were kidnapping women and forcing them to get pregnant so that the wife could have a baby boy to replace her stillborn. Unfortunately for the women, when it even worked they tended to give birth to girls.
Law and Order episode 8x14, "Grief" one of the more disturbing episodes of the series: a woman was accused of paying off a hospital orderly to impregnate her comatose daughter. A Downer Ending all around due to the fact that the daughter dies after delivering a healthy baby via C-Section. And the parents of the orderly sue for custody of the baby.
Doctor Who:
- In "The Doctor's Daughter", the Doctor is forcibly cloned at gunpoint. He's disgusted by it and considers his forced fatherhood this trope.
- A variant in the sixth season: While Amy's daughter was conceived on her wedding night with Rory, she spends the first half of the season actually being held captive by sinister people, not waking up until she was literally having contractions. Her consciousness was walking around freely in a duplicate body, and she spent nine months thinking her pregnancy test had just been a false alarm. And then her baby is kidnapped and raised as an assassin to kill her best friend.
Scorpius's origins on Farscape: His Sebacean mother was kidnapped and raped by a Scarran as part of experimental trials to create Scarran-Sebacean hybrids. Apparently Scorpius was the only one to survive. Despite his powerful intellect, due to his weak physiology (combing a Scarran's heat generation with a Sebacean's extreme vulnerability to that very heat) the experiment was deemed a total failure and the Scarrans marked the Sebaceans down as a species to wipe out rather than conquer and rape. Scorpius himself dedicates his entire life to making sure the Sebaceans wipe out the Scarrans instead.
- Also when the Scarrans attempt to forcibly transplant Aeryn's baby into Chiana.
Happened in an episode of Picket Fences where the doctor was trying to produce a "miracle" by causing a virgin to give birth to a child.
An episode of Law and Order SVU has this too. The team was called in when a doctor found that his comatose patient was pregnant. It turns out that other patients were also impregnated and given abortions to extract stem cells for stem cell research, mainly for an elderly rich man with Parkinson's who is desperate for a cure. The case ends with the comatose patient remaining pregnant, and the elderly man seeking parental rights in order to get access to the umbilical cord, which contains stem cells.