If you liked
Btooom!
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...then you might like
Danganronpa: Kibou no Gakuen to Zetsubou no Koukousei The Animation
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A large group of people are trapped in a death game and are forced to kill a certain amount of people in order to leave. At first glance, the male protagonist seems to be very average and normal, but they are soon shown to be very skilled in this particular situation. They are both flawed but really enjoyable series.
If you liked
Gin no Saji
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...then you might like
Shokugeki no Souma
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A boy goes to a special high school. Gin no Saji is about Hachiken trying to get used to the agricultural lifestyle, while Shokugeki no Souma is about Souma trying to become the best chef. They are both hilarious comedies involving delicious-looking food.
If you liked
Ouran Koukou Host Club
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...then you might like
Shokugeki no Souma
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School comedies about a "commoner" arriving at a prestigious school. Food plays a role in both of them, although much more in Shokugeki no Souma. They're both very entertaining.
If you liked
Gintama
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...then you might like
Kekkai Sensen
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They're both set in a modern city that aliens and humans inhabit. Both of them give off a feeling of randomness (at least judging from episode 1), although Gintama is more comedic. Zap and Hijikata have similar personalities and voice actors, same with Leo and Shinpachi.
If you liked
Mahou Shoujo Madoka★Magica
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...then you might like
Hunter x Hunter (2011)
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At first glance, they seem like pretty happy-go-lucky series to watch for fun and a bit of good action. As you keep watching, you realize that they're not happy series. Actually, they're closer to black holes. There's lots of drama, violence (more so in HxH), and dark concepts. They both have somewhat childish and misleading art and character designs. Main protagonist is a young naive person.
If you liked
Angel Beats!
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...then you might like
Death Parade
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They're both set in the afterlife, with one main character with amnesia and the other a white-haired emotionless person. There's a lot of drama concerning each character's past (more so in Death Parade) and some comedic moments (More so in Angel Beats!). I consider both of them masterpieces.
If you liked
Tegamibachi
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...then you might like
Hunter x Hunter (2011)
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In HxH, a young 12-year-old boy becomes a Hunter in order to find his father who was also a Hunter. In Letter Bee, a young 12-year-old boy becomes a Letter Bee in order to find his childhood hero who was also a Letter Bee. They meet many friends and enemies along the way. HxH is better than Letter Bee, in my opinion.
If you liked
Gintama
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...then you might like
Noragami
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I'm surprised that no one has recommended these two, because they have a lot in common. They're both about a person who was a badass in his mysterious past (Gintoki and Yato) who now runs around with two kids (Shinpachi and Kagura, Yukine and Hiyori) doing any job for money. Both are a great combination of action and comedy, although (in my opinion) Gintama is more comedy-oriented and Noragami has more drama.
If you liked
Gintama
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...then you might like
Lucky☆Star
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Great comedy anime with no particular storyline and lots of pop-culture references. Although they have very different settings, some characters are similar (Gintoki and Konata, Kagura and Kagami).
If you liked
Sword Art Online
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...then you might like
Akame ga Kill!
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The main characters are both young swordsmen who set out towards a place that they think will be wonderful, but soon discover the ugly truth about the place. Both Akame ga Kill and SAO involve fantasy creatures and lots of well-animated fights. Some of the character are similar: Kirito and Tatsumi, Klein and Lubbock, Silica and Mine. They both start out as great anime with lots of potential but soon deteriorate, but I think that if you can ignore the bad stuff you can enjoy both of these series. Oh and did I mention that there's a lot of kawaii girls?
If you liked
Fullmetal Alchemist
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...then you might like
Kuroshitsuji
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The story is set in England (well, FMA's Amestris is based off of England). The main character is a short teenaged boy with abnormal body parts is called a dog by the public (in FMA, 'dog of the military', in Kuroshitsuji, 'Queen's guard dog'). He's followed around by someone who is not your average human, and together they solve mysteries about their country. Both of them have great comedy and endings that don't stick to the manga.
If you liked
Fullmetal Alchemist
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...then you might like
Ao no Exorcist
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They main characters are two brothers. Ed is like Rin (hot-headed older brother) and Al is like Yukio (calm younger brother). Both have lots of comedy and feels too. There are many similar characters, eg. Winry and Shiemi, Hohenheim and Fujimoto. Neither of them follow the original manga story but they're still worth a watch (make sure you read the manga too though (there is also another version of FMA).
If you liked
Amagi Brilliant Park
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...then you might like
Barakamon
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The male leads both: - were famous/respected in the past but certain events changed that - are sent to a less-populated place that they don't want to be in - have a lot of character development over the series - meet new people who have completely different backgrounds to them - are kind of similar in age - are narcissists The plot, or, since Barakamon doesn't have much of a plot, the main idea of the story is similar. The MC gets sent to some random place that's completely different from what they're used to, and have to adapt to their new (and very interesting) friends/neighbors. The main difference between these two is that in Amagi Brilliant Park, Kanie is trying to save the park, whereas in Barakamon Handa is just staying their until he apologises.