If you liked
Sword Art Online
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...then you might like
Hai to Gensou no Grimgar
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A group of people are thrown into a fantasy world from which they cannot escape and must fight to find a way to survive. Though comedic at times, the plot is relatively serious and focuses on battles, life and death, and the bonds between characters. Both are also by A-1 Pictures, so their art styles are somewhat similar.
If you liked
Space☆Dandy
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...then you might like
Kekkai Sensen
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An episodic storytelling format, beautiful flowing animation by Bones, quirky background music and wonderfully-written characters are what make these two shows come alive. Both are short, 12-episode journeys through the everyday lives of the characters as they live and work alongside otherworldly creatures. Though generally lighthearted, both Kekkai Sensen and Space Dandy have enough emotional mini-arcs to pull at your heart.
If you liked
Kidou Senshi Gundam SEED
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...then you might like
Aldnoah.Zero
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A group of students finds themselves involved on one side of a war that is being fought between two races fueled by hate and fear. Trying to connect the two sides is a pacifistic emissary from the "enemy" side who eventually takes matters into her own hands once she learns the truth behind the motives of her allies.
If you liked
InuYasha
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...then you might like
Kamisama Hajimemashita
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Kamisama Hajimemashita is a little like a new-age Inuyasha. Both main female protagonists are regular high school students before they find themselves immersed in a world of youkai. In both cases, the main male lead is a youkai (dog in Inuyasha, fox in Kamisama Hajimemashita) who was once in love with the female lead's previous form/predecessor, as well as both female leads having a key plot object inside of them. Both female leads can travel back and forth through time as well as having to solve problems created by the youkai. Both also include a slow-moving romance between the male and female lead, based largely at first on the two characters trying to get along.
If you liked
Loveless
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...then you might like
Kurokami The Animation
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Though Loveless is arguably rather shounen-ai, both anime involve similar battle systems in that a pair is required to fight to maximize their chance of success, and that one part of the pair fights while the other provides power. Both anime also involve a shady organization that the main protagonists fight against.