If you liked
Kidou Keisatsu Patlabor: On Television
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...then you might like
Taiho Shichau zo (TV)
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Both are lengthy animes that are slice of life/police procedurals that revolve around vehicle action. The main point of variance being the police cars of 'You're Under Arrest!' TV are swapped out for police mecha in Patlabor TV. But the ensemble slice of life antics of a police department is strongly mirrored between these two shows, with the 'near future' SF setting/technology of Patalabor being the main point of divergence in the details.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Urusei Yatsura
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Both series have a girl with otherworldly abilities coming into the life of a luckless male protagonist, and subsequently turns these mild-mannered fellows otherwise hum-drum lives upside down. In both, the female protagonists regularly have otherworldly friends and rivals show up to cause havoc in their and their new significant others' lives with zany hi-jinx. Another shared dynamic is the poignant moments the couples share, even amidst the chaotic adventures both shows offer sincere sentiment and show these characters have strong commitment and affection for each other, even with all the madcap insanity.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Flying Witch
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Both are a perfect mix of slice of life and supernatural hi-jinx, with well defined & likeable characters brought to life with beautiful and clean animation designs . Both are slower paced slice of life comedies, with the chief difference being Ah! My Goddess leans more into romance, where Flying Witch is more comedic drama.
If you liked
Video Girl Ai
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...then you might like
Kobato.
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Both deal with ephemeral or liminal girls who fall in love with tragic male protagonists who both realize almost too late that the girl who was in front of them the whole time was the one they truly love. Both have fairly sad final plot arcs, but Video Girl Ai is more grimdark, whereas Kobato's offers more hope/a second chance in it's epilogue.
If you liked
Kimi ni Todoke
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...then you might like
3D Kanojo: Real Girl
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Both of these series feature outsider protagonists coming out of their shells through the development of a romance with a more outgoing significant other, with 3D Kanojo: Real Girl showing an introvert male paired with a more extroverted girl. Whereas Kimi Ni Todoke was an inversion of that formula featuring an introverted girl with a more extroverted boy. Both shows address social pressures and anxieties in regard to high school/developing young love with charming characters and compelling melodrama that immerses the viewers in their ongoing development.
If you liked
Urusei Yatsura
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...then you might like
Kobayashi-san Chi no Maid Dragon
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Both feature lots of great slapstick humour and very likeable female protagonists. Urusei Yatsura is more toward aliens/science fiction as a major series theme, and Miss Kobayashi's Dragon Maid is focused on the supernatural/fantasy elements. Both stories actually have some very compelling romantic moments with lots of dramatic punch/depth and significant others that are both merely mortal, but interesting characters with depth in their own right. And both shows have utterly bonkers OPs, both are hard to skip LOL!
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Kobayashi-san Chi no Maid Dragon
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Both shows fit the Magical Girlfriend genre with both mortal protagonists receiving a romantic surprise in the form of an immortal being who falls into their life almost by accident. Both shows have large ensemble casts with lots of interesting personalities and pulse with loads of slapstick humour and magical hijinx. Both are heartwarming stories of unconventional family units forming when the human world overlaps with the supernatural and have lots of poignant & tender moments between the leads.
If you liked
Chuunibyou demo Koi ga Shitai!
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...then you might like
High Score Girl
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Both series are focused on growing romantic relationships between somewhat socially inept pre-teen/teenaged protagonists (which makes for great moments of awkward humour). Well summarised as 'learning to love' in both situations young male protagonists, both lacking in average social graces, meet insular young girls who find kindred spirits in boys who share/understand their offbeat hobbies. With the undercurrent of both shows focusing on the change in perceptions of these female protagonists as they grow from annoyances to object of genuine affection to the male protagonists. The adage 'sharing is caring' comes home to roost in these shows, as romance blooms in shared worldviews of the main characters and the friends that surround them in their stories.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Aria the Animation
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Both shows deal with a very serene and joyful heroine surrounded by caring friends. Many episodes in each show are slice of life drama with the protagonists meeting new people and learning more about the world and themselves through these rewarding encounters. Both shows have gradual, but steady and meaningful character growth. And last but not least, the two sweetest & kindest Anime heroines you will ever meet, Akari (ARIA) and Belldandy (Ah! My Goddess), great protagonists!
If you liked
Chobits
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...then you might like
Air
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Both deal with female protagonists with a haunted past, and involve a male protagonist who sets out to help said female lead achieve some kind of happiness in their lives, where they go with their resolutions is where these two shows are markedly different from each other.
If you liked
Air
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...then you might like
Kobato.
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The parallels between Kobato & AIR were striking, both deal with a female protagonist trapped in a death/rebirth cycle and a male protagonist who intervenes in the situation to help offer resolution. The major difference being the resolution of each, as one chooses a tragic pathos-laden ending and the other offers a more uplifting plot turn in it's epilogue.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Air
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The issues of fate & destiny are strong core elements in both shows, however Ah! My Goddess has much better character development thanks to having 50 episodes, but lacked the clean, if not tragic resolution of AIR, possessing a more positive open-ended ending.
If you liked
Air
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...then you might like
Kowarekake no Orgel (Movie)
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Both deal with female protagonists consigned to a tragic ending. The parallel between the final arc of AIR and the story of Kowarekake no Orgel is fairly direct, with the only major difference being that AIR deals with a child-parent relationship whereas Kowarekake involved a sibling-type bond.
If you liked
Wish
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...then you might like
Kobato.
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Essentially 'Kobato' is a mashup CLAMP adaptation, with Wish's Angel protagonist Kohaku playing the role of a recurring supporting character in Hanato Kobato's story, with her and her lover crossing paths at various points in the series with Kobato.
If you liked
Chobits
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...then you might like
Kobato.
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Lots of crossover locales, characters, and thematics that link these two CLAMP titles and both feature growing romance in the heart of an otherworldly & mysterious girl. On top of that Kobato also served to be a combined adaptation with the older CLAMP manga title 'Wish' with Kobato regularly crossing paths with the 'Wish' protagonist, Angel Girl Kohaku and her live-in lover, in the Anime & Manga. Herself receiving some decent spotlight time during the Kobato series run, being especially pivotal in some of the exposition in the final run of episodes. Chobits and Kobato were both well animated by Madhouse, who I really enjoy the work of personally.
If you liked
Aa! Megami-sama! Movie
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...then you might like
Tenchi Muyou! in Love
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Both films feature massive stakes with the fate of existence itself hanging in the balance in both cases. In addition both films feature effective moments of romantic drama, well-balanced with exciting action set-pieces. Both film were exemplary theatrical animes for their respective franchises and stand up well over repeated viewing. Well worth a fans time to check either film out, I would recommend them to any fan.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Kobato.
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Both definitely fit the mold of the modern Magical/Mysterious Girl formula created by Urusei Yatsura years ago. Both feature mysterious otherworldly women who come to Earth on a mission and end up falling in love with all the consequences that it entails for their lives and lovers. I think many fans of Hanato Kobato or the Goddess Belldandy will likely find the other appealing, I heartily recommend either to fans of SoL, Romance, or Magical Girl Animes, both also contain elements of Supernatural/Divine drama as well.
If you liked
Aa! Megami-sama! (TV)
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...then you might like
Chobits
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Another example of the magical or mysterious girl concept. Both series deal with 'fish out of water' female protagonists who come across as naive, but in matter of fact are both powerful entities with the immense power to affect massive changes in both of their respective worlds. But despite that both shows spend a lot of time on romantic development between mortal men and these mysterious women who enter their lives and alter them irrevocably with relationships which are far from the conventional they seem to be at first glance. A great example of these deeper implications shared between the two shows is the mortal man paired with an immortal female entity for instance, which is pushed back at by the implication that love can conquer these kinds of differences. This is just one way in which these shows examine the deeper meaning of love that can transcend differences between sentient beings regardless of heritage/origin.