If you liked
Shingeki no Kyojin
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...then you might like
Owari no Seraph
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They're basically the same thing with different enemies. Post apocalyptic setting with humanity inside a wall to keep the bad guys out. The main characters are the squad of badasses that venture outside the walls and kill the bad guys. The main characters are basically the same dumb-as-rocks, brown-haired, green-eyed, slightly-shorter-than-average, sixteen-year-old boy, hellbent on revenge against the bad guys, though Eren is slightly dumber. There's also the mentor character who is way more badass than the main crew (Levi/Guren), the tall, short-haired rival of the main character (Jean/Shihou), the sweet, adorable, best friend of the main character (Armin/Mikaela and later Yoichi), the girl that follows the main character around and happens to be a total badass (Mikasa/Shinoa).
If you liked
D.Gray-man
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...then you might like
Owari no Seraph
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Both series have an organization of superpowered badasses that fights evil creatures, and the other side is your typical evil monsters that have some sort of royalty ranking system and are generally sinister. There's also the five man band of main characters, and then a few others who fade in and out. The most striking similarity, however, is the general vibe. It's dark with some lighthearted moments. Not to mention the uniforms are very much similar.
If you liked
Arslan Senki (TV)
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...then you might like
Akagami no Shirayuki-hime
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These two animes are nothing alike but Zen IS Arslan in 4 years. They look and act exactly the same, and they're both princes with an unfortunate family situation. Past that, the shows are completely different. One is a slice of life shoujo romance and the other is full of action, large scale battles, political scheming, and violence.
If you liked
Akatsuki no Yona
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...then you might like
Akagami no Shirayuki-hime
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Both involve a rare redheaded girl who cuts her hair and escapes a bad situation and finds a group of warriors, including some kind of bodyguard (Hak in Yona)/protector (Zen in Shirayukihime) who they fall in love with along the way, as well as a strong focus on characters and character development, with a cast of interesting, lovable characters. Both heavily involve politics and royalty, and a reverse harem, though it's less obvious in Shirayukihime. Yona focuses more on action/adventure and fantasy where Shirayukihime is more slice of life and has no magic. Likewise, neither is particularly dark, but in different ways. Shirayukihime is romance and pleasant slice of life, were Yona has a lot more comedy and silly characters.
If you liked
Log Horizon
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...then you might like
Hai to Gensou no Grimgar
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Similar 'trapped in a fantasy game' concepts with a focus on the characters and world rather than action/adventure, where most of the main characters are all part of a guild or party. Both have elements of memory loss as well. There is one very major difference which is also a huge spoiler to LH, which affects both stories quite a bit. Basically, the plots are extremely different, but the settings, themes, and characters are almost identical.
If you liked
Darker than Black: Kuro no Keiyakusha
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...then you might like
Psycho-Pass
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Both have similar themes and a similar feel. Kirihara and Tsunemori have a lot in common, and Hei and Kogami are practically the same character, to say nothing of the similarities between Huang and Masaoka. My point is, though they are on different sides of the law, the main casts of both shows are similar, the shady organizations they work for have the same secretive, questionable feel. Moreover, both series have very well done villains and no one is evil for the sake of being evil.