If you liked the InuYasha anime, the Anime-Planet community thinks you'd like:
When Tokidoki Rikugou donned a pair of virtual reality glasses and entered a Bakumatsu-era exhibit at a museum, he had no idea that his life would drastically change. While walking across a bridge in the fabricated reality, Tokidoki ran across a small being and a monster called a nue - and he was promptly attacked. His eye was damaged, but more importantly, Tokidoki discovered that he was now stuck inside the "virtual reality" filled with samurai and spirits. Now, with the help of Kuchiha, a warrior woman possessed by a dog spirit; and Shinonome, a fellow student who has been stuck, just like Tokidoki, for the past two years, Tokidoki must search for the truth behind the nue and try to find a way home.
With both InuYasha and Amatsuki a person (Kagome in InuYasha and Amatsuki in Amatsuki) are pulled into a strange world in the feudal days. Both encounter monsters and demons along the way in which they have to find people to help them defeat the demons and go back to their own world. Each series has the same type of feeling to them.
Marina is a fifteen-year-old mermaid who lives at the bottom of the sea; alongside her sisters, loving father and dolphin friend she explores sunken ships and gazes at human treasures, all the while longing to see the outside world. In secret, Marina swims to the surface one evening and sees a beautiful prince that she instantly falls in love with – but the evil sea witch uses her powers to sink the prince’s ship, casting him into the cold water below. Marina saves her love but remains hidden while he comes to on the shore, leaving her yearning to see him again. To fulfill her desires Marina visits the sea witch and exchanges her beautiful singing voice for human legs – but there’s a catch. If the prince marries another, the morning after Marina will die of a broken heart and will turn into sea foam...
These two titles are both similar because their plots revolve around a girl who falls in love with a man from a land far away from her own. Just when these girls think they have gotten close to the guy that they like, they realize they are part of a love triangle.
In the fantastical land of Amawakumi, a succession ceremony occurs each 30 years to pass control of the kingdom to a female heir of the Hime clan. But three decades ago, the Hime clan was unable to produce a daughter and was warned that if history repeated itself, the entire clan would be purged. Now faced with the same problem in the present, the Hime clan opts to send their disguised son Arata to the ceremony instead, unaware that he’d be sent into a trap where the former princess is murdered and the boy would be framed for the crime. Meanwhile, on Earth, Hinohara suffers a similar sense of betrayal at the hands of his classmates, and after wishing he could just disappear, he and Arata switch bodies. Now, as Arata struggles to find a way to return the two to their own worlds, Hinohara must try to escape capture, clear Arata’s name and fulfill this princess’s last wish by exposing her killers.
Both of these anime are about a modern Japanese high school student who is teleported to a dangerous fantasy world. Both Kagome and Arata are given magical powers and they must travel around this new world, along with new friends, to help save it. They both have a similar feel and I think if you enjoyed one, you'd enjoy the other.
Three shrine maids have a distant cousin who moved away for schooling when they were young. Years later, he returns, and the three girls are tasked with protecting him. During this, the eldest (who's a teacher at the school) and the middle one form a "Miko" council. The story goes through their growth together and their battles with the servants of the Evil God.
There is a legend of an angel who fell to Earth many years ago, and was forced to marry a man because he held the key to her only way home. Hundreds of years later, sixteen year old Mikage Aya is the reincarnation of Ceres, the vengeful angel, who must now fight for her life against her family and her own twin brother Aki, the reincarnation of her past evil husband...