If you're looking for anime similar to InuYasha: The Final Act, you might like these titles.
While reading "The Universe of the Four Gods", best friends Miaka and Yui are mysteriously transported into a strange world full of magic and unfamiliar faces. As if their arrival was determined by fate, Miaka is revered as the Priestess of Suzaku, the savior of their warring country, who was destined to arrived in a flash of light, from a land far away. Betrayal, love, and heartache accompany this fantasy-filled tale of friendships torn apart, and hope that never fades.
In the revolutionary Meiji period, Japan is undergoing enormous political change. It is a time when vagabonds and terrorists will use any method to prevent the modernization of their country, even if it means trampling on the innocent in the process. In such a time, Himura Kenshin, a wandering samurai, has dedicated his life to protecting the weak and desperate peasants from those who would oppress them. However, Kenshin has a dark past which threatens to destroy the values he is fighting for. When he meets his new friends Kaoru, Sanosuke, and Yahiko, and tries to build a peaceful life with them, events conspire against him. Can Kenshin overcome the demons within and without, and finally ensure the peaceful future that Japan deserves?
Both shows involve awesome sword fighting, special swords, out of this world characters, the past, humor, love, and some darkness. Both Kenshin and Inuyasha have times when they become a darker side of themselves. For Inuyasha, it's when he turns demon. For Kenshin, it's when he becomes or nearly becomes Battosai the manslayer. Both have romance, though moreso in Inuyasha. Both also have plenty of comedy. In moods they are very similar. If you like one, you will probably like the other. The enemies in both shows are supernatural. In Inuyasha, it's demons. In Kenshin, it's other strange things. The action in both is exciting. The sword battles are awesome. If you love one, you will probably love the other.
Nanami used to live in a ramshackle apartment with her father - a man who spent half his time gambling and the other half hiding from debt collectors - until one day the scoundrel ran away, leaving his daughter hungry and homeless. That is, until she meets a mysterious stranger in the park who deems her the new goddess of a local shrine! Unfortunately, Nanami’s new home is occupied by Tomoe, a fox familiar who objects to the presence of a mere mortal and immediately begins to bicker with the girl. If she can manage to form a contract with the troublesome man, he’ll be obligated to accept and help her perform her duties. But there’s a catch: Nanami has to kiss him first, and who’d want to lock lips with that awful guy?!
Ranma, raised to be a man among men, has a bit of a problem: he is half woman! While training in China he fell into a strange magic spring at Jusenkyo. Now, he is eternally cursed to change into a beautiful woman whenever he is hit by cold water, but that may be the least of his problems; his father has betrothed him to marry! There's never a dull day for Ranma as he attempts to find a cure for his curse, train to become stronger, and grapple with the fact that half of himself may be more feminine than his fiancée!
Although the Plot is way different, the characters are not, as both are created by the same author, "Rumiko Takahashi" and she kind of re-use some of the same character designs and personalities:
Ranma = InuYasha
Akane = Kagome
Ukyo = Sango
Ryoga = Koga
Both have the same feel for the interactions with the characters and although Ranma is more comical, you can see it as a stepping stone for what would become InuYasha.
Chiaki is an energetic young teenager who lives with her grandmother in an old temple just outside of town. She is a descendant of the powerful sorcerer Enno Ozune who, along with a powerful guardian spirit, protected the land from evil monsters. Now, sinister forces have begun to arise again and search for the Seeds of Evil. When their temple, which hides a Seed of Evil, is attacked, Chiaki releases the seal on the legendary guardian spirit Zenki to protect them - but he's stuck in the form of a child until she unleashes his power with the Guardian Bracelet of her ancestor. Together, the duo must defeat the evil Karuma and his minions while destroying all the Seeds of Evil. Can Zenki and Chiaki learn to get along and fight as a team, or will their constant arguments be their downfall?
These animes are about the same and even have the same group of characters, although Zenki is episodic, with a monster of the week and InuYasha is far superior with an epic story that moves forward with every chapter. You could say that Zenki is a bad copy of InuYasha, except that this anime happen much earlier in time.
Suzuko and Shu are siblings who live in an undetermined part of Tokyo. While walking together one day, an explosion suddenly occurs, and Suzuko awakens in an unfamiliar place: the past. The time is during Japan's civil war, and the faces are anything but friendly. With the help of newly-met Shukumaru, Suzuko must unravel the mystery of her disappearance and discover the connection between these two worlds, while trying to figure out how she can return to her own time and place.
After mysteriously being sent back in time, Shin-chan saves the life of Matabe Ijiri, a samurai who leads the army of a small province in Japan. Welcomed as a guest by Ijiri, Shinnosuke must figure out why he is stuck in 1574.
Due to some unlikely events, Saburo is flung back in time to the Sengoku Era. In the past, he meets a young, but sickly Oda Nobunaga, one of Japan’s greatest war lords. Unable to shake Saburo’s uncanny resemblance to himself, Nobunaga asks Saburo to take his place as war lord. Equipped with knowledge from the modern era, will Saburo be able to unite Japan?
Ordinary high schooler Yoshiharu is sent back in time to the Warring States Period, however not the same time line that he remembers. There he meets Nobuna Oda - not Nobunaga, Nobuna. In this world, all the famous figureheads and warlords of the era are female! Nobuna teams up with Yoshiharu to help fuel her ambition and quest to rule the world…
Professional wrestler Genzou Shibata was preparing for his next match, when suddenly he was summoned into another world. He's asked to defeat the magical beasts that roam the land, but as an avid animal lover, Genzou would rather help these creatures. So after a short stint as a hunter, the man opens the Kemono Michi pet shop. There, along with his part-animal employees, he hopes to adopt out rare beasts and foster a pet culture in his new home.