Dream Hunter Rem (jp. ドリームハンター麗夢
, Rem the Dream Hunter) is an adult comedy OVA consisting of six episodes across multiple projects. The original run of the series aired from 1985-1987, and only consists of four episodes. The other two came out in the 1990's and are self-contained stories.
People tend to hear about Rem due to its very first episode. The OVA originally was going to take a more pornographic direction, but it was toned down when its popularity proved to be more than they expected. For home releases, this episode was later edited to follow the more tame nature of the rest of the series. More on this later.
Ayanokouji Rem is a private investigator specializing in the supernatural. Unlike other investigators, though, she is a 'Dream Guardian', entering the dreams of other people to save them from ghosts. Rem comes from a long line of these guardians, and they often have no dreams of their own—this makes them able to enter the dreams of others with ease.
While Rem is a normal young girl in the waking world, she is a strong warrior in the world of dreams. Her and her pets Alpha and Beta (who have the same powers) go place to place helping those with supernatural problems. While the story mostly follows her, other supporting characters include Sakaki Junchiro, a detective she regularly cooperates with, and Enkou, a monk who offers his assistance in the waking world.
The 1987 OVA is somewhat episodic, however there's enough of an overarching plot to require the episoes to be watched in order. The first episode involves the daughter of Inspector Sakaki, who is possessed by an unknown supernatural monster, making it extremely difficult for her to sleep. The second episode focuses on the evil Dr. Shinigami (also referred to as Mephisto)—he has the same powers as Rem, but is using them instead to kill people, rather than help. In the third episode, Rem goes undercover in all all-girl's school after hearing about ghosts haunting the place. The final episode focuses on the ghost of a vengeful samurai who lost his lover—who Rem just so happens to be the reincarnation of.
The 90's OVAs introduce one-off characters in each episode. Some time between the final episode in 1987 and the 1990 OVA, Rem meets a young girl named Mina who can't walk due to an illness, but travells dreams the same way Rem does. Unfortunately, a woman known only as the Masked Witch is going after both Rem and the girl, and it's up to the both of them to stop her.
The 1992 OVA is a Rem-style retelling of Frakenstein. Victor Frankenstein (not to be mistaken for his ancestor, Victor Frankenstein) creates a handsome artificial human by the name of Julian, who is a very upstanding and kindhearted young gentleman. Unfortunately, Dr. Shinigami leads the boy to the dark side, and turns into the Frankenstein's monster one may be familiar with. It's Rem and co.'s job to make sure he doesn't cause any disaster, as well as assuring the safety of a little girl Julian has befriended—a blind girl named Sherry.
In the first episode of Rem, Sakaki's daughter is naked, masturbating, and shown to be practically molested by bugs in her sleep. The monster haunting her dreams takes the life force and of women by having sex with them, and Rem is almost raped by it herself. However, she quite literally uses her pussy to fight back at him, basically shooting a laser out of her crotch among other things you'd expect from an old hentai.
The Laserdisc and VHS versions of this episode, considered Special Edition, instead put Sakaki's daughter in a nightgown, and take out the masturbation element entirely. Similar happens with Rem in the dream world, with them having taken her pussy power away. While the hentai version of Rem never received a home release, copies of it exist online and can be watched freely.
Nearing the end of the original OVA's lifetime, the soundtrack was released on vinyl and cassette in 1986. The entire thing is available on YouTube, however it's not the best quality. There are many sections of music that aren't labeled on the release, either, which are noted in either the video's description or comments.
Due to the OVA not ending until 1987, the fourth episode's ending theme is missing. However, it seems like there have been multiple home media releases of the soundtrack (and other Rem-related audio) since, so it's probably out there somewhere.
Despite the series' relative obscurity, Rem occasionally appears in other media. The most recent appearance I can find is in Super Heroine Chronicle, released for the PlayStation 3 and PSVita systems in 2014.