If you liked
Shamanic Princess
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...then you might like
3x3 Eyes: Seima Densetsu
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They're both pretty short OVAs packed with action and magic. They incorporate mythology and philosophy with a bit of a twist (the second 3x3 OVA has more of these elements than the first). Unforeseen twists at the end in both shows. 3x3 Eyes has a better fleshed out story, more character investment & action (also gore). Shamanic Princess has a dreamier, art nouveau-esque style and a greater focus on magic. There is a romantic core around which both stories evolve. This is a more innocent love in 3x3 Eyes complicated by circumstance and a more mature, grown-up sort of love in Shamanic Princess. There is a bittersweet element to both shows' romantic arcs.
If you liked
Air
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...then you might like
Kamisama ni Natta Hi
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Both shows will make you laugh and cry. They start out deceptively normal (for an anime) and then the Key twist shows up and drives a knife into your heart. A lot of characters in both shows are surprisingly mature, deliberately acting out for the giggles. The main message, when you're done with the show, is actually rather somber. "Air" has better pacing and script, which is helped by the rather sparse day-to-day existence in the settings it depicts. "Kamisama..." is actually quite relevant to modern life but the same modern setting makes it comparatively cluttered in terms of everything that gets included in the story. Enough creative liberty is taken to avoid getting bogged down by the most complex parts but the pacing is still affected. Unlike "Air," "Kamisama..." does not have as many parallel stories that serve as distractors or build-up (as "Air" was a VN first) but both have detailed backstories for supporting characters.
If you liked
Denpa Onna to Seishun Otoko
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...then you might like
Kamisama ni Natta Hi
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One female MC claims to be an alien, the other claims to be a god. The male MC thinks she's crazy but indulges her fantasies. There are creepy moments where viewers and characters will feel like a ridiculous claim some character is making might actually be true (and who knows, it just might!). "Denpa..." has weirder characters and more overall chaos but feels more like a standard teen romance. "Kamisama..." tries to keep things under control and within budget but I'm not sure whether I'd say the theme is romance or friendship/family. The pace meanders and there are big twists in both shows but those twists are placed at different points along the storyline and that really makes a difference to the mood of the story because the placement affects the available time and even the necessity of expositions and explanations (!!both scripts have differently evil authors!!). "Denpa..." is a car full of loud and whacky weirdoes who shouldn't even have a driver's license riding on a smooth highway. "Kamisama..." is a car full of mostly-stable people driving along a treacherous mountain path. At the end, you'll be glad everyone mostly managed to make it out alive. But you might not get an explanation about how!
If you liked
Nagi no Asu kara
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...then you might like
Kamisama ni Natta Hi
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"Nagi..." and "Kamisama..." have the same overarching plot structure and emotional themes when it comes to how the relationships between characters develop. In one, the fantasy twist is that the female MC is a god, the other has people who can breathe underwater. Both shows explore these special elements to some depth and they bring people together and drive them apart too. "Nagi..." has slightly better animation and art (opinion) and the story is handled much more delicately (but it takes a different direction that requires that delicacy for the show to have any impact). "Kamisama..." can sometimes come off as preachy or cliche but the direction it takes is much more mature so I can't really fault them for taking the approach they did, considering that the show is only 12 episodes long. If either of these left you feeling like you want to watch something else like it, you should watch the other.
If you liked
Shinreigari
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...then you might like
Mayoiga
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Both are kinda trippy shows that make you question your own perceptions of the world if you get involved enough. Slow pacing, initially confusing, and there is a lot of attention paid to the details of characters' subjective perceptions and experiences and how they overlap with those of others or not. Mayoiga has considerably stronger Action elements than Shinreigari. Shinreigari has a stronger real-life based theoretical grounding for its world building and I had a field day on Wikipedia because of many of the things said in the voiceovers for the episode previews. Both shows have many easter eggs and unspoken connections. Shinreigari has more communicative characters who will eventually join enough of the dots for the viewer, but that is not the case with Mayoiga so it's more important to watch the latter particularly attentively or you'll miss out on the full experience & also get left confused as to wtf it was all about.
If you liked
Utawarerumono
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...then you might like
Seirei no Moribito
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Both have a very similar vibe. Similar focus on world-building & uncovering the past alongside political turmoil. They both left me feeling much the same emotions at the end. Strong themes of family/belonging & studying the nature of leadership/government. Both have nice soundtracks. Major differences would be that Utawarerumono is more explicitly violent (R17) while Seirei no Moribito has more performative fight scenes (R13); the personal revelations about specific characters are different in nature (Balsa's past is something she only chooses to reveal later in the series, but Hakuoro just cannot remember & searches for his past); & the nature of the political turmoil as well as the characters' roles in it are different.