If you liked the Asatte no Houkou anime, the Anime-Planet community thinks you'd like:
Once every thousand years, the Millennium Comet dances across the sky; and with it comes Jirachi, a legendary Pokemon able to grant wishes. Ash, Brock, May and Max have arrived to the Millennium Festival - headlined by a circus led by the Great Butler - but little do they know that danger awaits. Someone is plotting to steal Jirachi to accomplish their own selfish dream - to finally capture the mysterious Pokemon Groudon - and it's up to Ash and his friends to save him!
In these 2 animes, the plot revolves around a wish or in Pokemon's case, it revolves around a wish maker, but wishes nonetheless.
Without knowing what the consequences would be or without knowing that their wish would even be granted, they wish for what they want.
But soon after the wish, they run into trouble. In Pokemon, they must protect the wish maker from being used in the wrong hands whereas in Asatte no Houkou they must try to find a way to reverse the wish.
Morimiya Yorito is a normal student who has an abnormal obsession for the sky. One day, he meets a strange girl named Shihou Matsuri who shares his interest, but as fate may have it, she isn't a human; Matsuri is a Yaka -- a "woe of the night" -- who is immortal and cannot stand the sunlight. A strange man is chasing Matsuri, to use her powers, so Yorito decides to help her hide. What are the strange man's plans, and what secrets does Yorito's sister hide?
Makoto Konno is a somewhat foolish and tomboyish high school student who spends most of her time hanging out with her two male friends. Things change one day when she suddenly gains the ability to leap through time! At first, she uses her newfound ability to do things such as preventing her sister from stealing her dessert, cheating on a test, and singing Karaoke for 10 hours. However, the small alterations she makes to the timeline turn out to have unforeseen consequences that snowball into dramatic and lethal situations for her and those around her...
Both "Asatte no Houkou" and "The girl who leapt in time" are coming-of-age stories. Heroines discover that making mistakes and wishing to right them is only human, but the way to deal with errors is not easily acceptable, and planning one's future as one sees fit isn't necessarily the best thing for her.
Tatsuhiro Sato is a university dropout and a "hikikomori" – a person suffering from social withdrawal. To Sato’s dismay, his self-imposed exile from the world is rudely interrupted when a mysterious girl knocks on his door. She has charged herself with the task of curing Sato of his hikikimori ways! Now, as new problems ranging from hentai games to internet suicide spring up, can Sato manage to overcome his hermit-like ways, or will the imaginary N.H.K conspiracy force him to remain a hikikomori forever?
Asatte no Houkou and Welcome to the NHK are two anime that serve as prime examples of strong character development. They each focus in on a core set of characters as they try to cope with their flaws and search to find their place. Although NHK's harsh social commentary gives it a very different feel compared to the lighter tone of Asatte, they're similar enough at their core so that fans of one should be fans of both.
Kazuhiro Uchida has always dreamed of becoming a fighter pilot, but has been forced into the helicopter-training program instead. Embittered and discouraged, he still completes the training and is given his first position in a helicopter rescue unit. The catch? It’s located in a new town, far away from his loved ones. But the job of a rescue worker is incredibly demanding, both mentally and physically, and Kazuhiro’s less than enthusiastic attitude just won’t cut it. In order to succeed in his new career, Kazuhiro must survive the harsh reality of rescue work, and rediscover his dream.
People who liked "Asatte no Houkou" would also like "Rescue Wings". Both series are very "slice of life" and deal with normal people doing normal stuff. The reason for suspense is different (wish coming true against fighting bad odds to rescue endangered persons), but the main characters grow by their experiences and in the end, the resolution of the stories are nothing extraordinary in particular, but leave a lasting memory.