If you liked
Shinryaku! Ika Musume
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...then you might like
Zoushoku Shoujo Plana-chan!
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Cute little water-creature girls with tentacle-like hair. Similar comedy and art styles as well.
If you liked
½ Prince
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...then you might like
Magic Insulator
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Both of these are amusing manhua with fantasy themes and similar art.
If you liked
NHK ni Youkoso!
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...then you might like
Oyasumi Punpun
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Both deal with individuals surrounded by people and situations that are rather psychologically twisted. Both contain very similar types of dark/morbid humor, and main characters with rather "lively" imaginations. The lead females (Aiko/Misaki) also have very similar issues and situations.
If you liked
Natsume Yuujinchou
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...then you might like
Hyakki Yakoushou
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Both involve people who have a "gift" that enables them to view spirits (not to mention not entirely friendly spiritual "guardians"). Natsume Yuujinchou seems to be a more shoujo variation on the themes of Selected Pandemonium, which is aimed squarely at an adult audience. Both are well worth a look if you like stories about the Japanese view of the supernatural.
If you liked
Mushishi
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...then you might like
Hyakki Yakoushou
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These are probably the best two mature supernatural titles out there. Both have excellent artwork and engaging, if episodic, stories revolving around two men who have a "gift" that gives them a view into unique and mysterious worlds unseen by most people.
If you liked
Nodame Cantabile
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...then you might like
Piano no Mori
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These are both about young musicians and how they encourage each other grow and develop their musical talents. They feature a similar pair of lead characters: one is a rigorously trained perfectionist and the other is a free-spirited natural talent. Also, classical music plays a large role in Nodame and Piano no Mori.
If you liked
Sayonara Zetsubou Sensei
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...then you might like
Mangaka Chou Zankoku Monogatari
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These manga are both great examples of Japanese black humor. While SZS takes aim at a wide swath of contemporary Japanese society, Super Cruel focuses on the specific world of manga-ka. Both have a style of humor that can be vicious or vulgar (especially in Super Cruel), but if you enjoyed one of these, the other is definitely worth a look.
If you liked
Alien 9
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...then you might like
Bokura no
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Both deal with a group of children thrust into dangerous and traumatic situations because they have been "chosen" to protect their world.
If you liked
Gintama
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...then you might like
Oh! Edo Rocket
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Both series take place in bizarre alternate universe late-Edo-period Japan after the arrival of aliens. Both series have random, crazy humor and very entertaining characters. Oh! Edo Rocket has more actual plot and drama though. Also both feature the talents of Kugimiya Rie (Kagura/Shunpei).
If you liked
PetoPeto-san
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...then you might like
Mokke
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Both series are set in the countryside, and follow the daily lives of children. They have relatively lighthearted supernatural themes about the magical/spiritual world as a part of daily life.
If you liked
Kyou no 5 no 2
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...then you might like
Minami-ke
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These are both works by Sakuraba Coharu, and they share a similar sense of humor. Both series revolve around school age children and their comedic interactions, but they are intended for an older audience. Sakuraba gets a lot of laughs out of a class of fifth graders on the cusp of puberty in Go no Ni, but the wider age range of characters in Minami-ke and the great dynamic between the three Minami sisters allows for even more variety of hilarious situations. If you enjoy one of these manga, you'll almost certainly enjoy the other.
If you liked
Sayonara Zetsubou Sensei
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...then you might like
Katte ni Kaizou
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These series have the same manga-ka. Sayonara Zetsubou Sensei is the later work, and is a major improvement in both comedy and art over Katteini Kaizou. The humor is darker and geared at an older audience. If you enjoyed Katteni Kaizou, you'd probably love Zetsubou Sensei.