Monster girl anime is a niche genre that's started to make its way into the mainstream. These shows feature girls and women who aren't exactly human - instead, they're centaurs, demons, dullahans, vampires, zombies, and all manner of mythological beasts.
More often than not, they're overtly suggestive, totally adorable, or some combination of the two. Monster girls in anime commonly befriend male humans. Soon enough, the man finds himself surrounded by a harem of them.
The genre has a lot of crossover with ecchi, harem, and other related genres, and it tends to include a lot of fan service - Monster Musume and Rosario + Vampire are well-known examples that follow this trend. There are also shows, including A Centaur's Worries and Interviews With Monster Girls, which use monster girls to explore social issues.
Whichever tone you prefer, if you like your anime with some fantasy sprinkled into it, you'll probably find something you enjoy in the monster girl genre.
This series is unique, as it's one of the few harem anime in which the male protagonist avoids becoming entangled with the women surrounding him. It makes sense, given protagonist Kimihito Kurusu's harem comprises centaurs, lamias, and dullahans; in addition, interspecies intimacy is strictly forbidden.
How will Kimihito survive the onslaught of busty monster ladies who all want a piece of him? You'll have to watch Monster Musume to find out.
Interviews With Monster Girls is about a biology teacher who tries to learn everything he can about demi-humans - which are half-human/half-monster beings that exist in this universe. Specifically, he's interested in his three students: a dullahan, a snow woman, and a vampire. Add to the list his succubus co-worker.
The show uses the girls' demi-human status to reflect real-world discrimination, particularly in regard to accommodations for students with special needs in schools. For example, Machi, a dullahan, must carry her head around with her everywhere she goes, which means she needs to use a backpack instead of the regulation school bag. One plotline revolves around her teacher advocating for her backpack use on the basis of her physiology.
When computer programmer Miss Kobayashi befriends a dragon named Tohru, she ends up with a live-in dragon maid who's also madly in love with her. Through Tohru, Miss Kobayashi meets all kinds of other dragons.
They even meet a child whom they end up adopting, as well as an exiled dragon goddess.
Issei Hyoudou is a teenage deviant who wants nothing more than to have his own harem of fawning women. One day, a beautiful girl asks him out. He thinks his dreams might be coming true, but then she slays him.
Fortunately, Rias Gremory comes to the rescue and revives him as her servant - then forces him to join the school's Occult Research Club. He battles angels and devils in order to survive. Most of the girls in this anime are just as beautiful as the initial slayer angel, but many of them are demons, angels, or other beasts.