If you liked the Welcome to the NHK! anime, the Anime-Planet community thinks you'd like:
After saving Japan from a missile attack, Akira Takizawa erased his own memories and disappeared, leaving a simple message for Saki: he’ll be waiting in the place where this all started. Having searched for him for some time with the help of Kazuomi, Onee and the rest of the gang, Saki finally determines that Akira is in New York City and heads there to find him. However, the rest of the Selecaos are also looking for Akira, and not everyone is happy about his impending rise to become the King of Japan...
Both of these shows are beautifully animated, involve conspiracy theories (though to differing extents), and are set in modern day Japan. Of course they both offer a love story, as well as a good mix of drama and comedy. But the thing that makes these two the most alike is their commentary on current events in Japan, particularly with the age gap and NEET/hikikomori phenomenon.
Naota Nanbada is a boring young boy who leads a boring life in a boring town. His older brother has left for America, and the closest he comes to any excitement is when his deadbeat dad has too much sake. But things change one day when a bizarre girl zooms up to him on a scooter and smacks him in the face with her guitar. What's more, once Naoto returns home he discovers that this strange woman has arrived ahead of him and moved in! Not only does she constantly engage in perverted activities with Naota's father and flirt with the young man himself, but she also claims to be an alien who is searching for the ‘Pirate King.' Now, Naota must learn to live with this new intruder, deal with an odd government agent who sports exceptionally large eyebrows and the mysterious Medical Mechanica, and come to terms with the fact that there are a variety of robots and weapons emerging out of his head - amongst other things. Perhaps boring wasn't so bad after all...
How interesting that this recommendation hasn't been proposed; as there is an obvious and fundamental similarity between these two anime that will make them appealing to either audience.
The development of love for someone, based on everything wrong in their life.
Major characters in these anime come to love each other by way of the negative aspects of their intrest's life. It's simultaneously baffling, yet completely understandable. Therein lies the enjoyment of these anime. You fall in love with these character's issues, too. There's comedy, sadness, bittersweetness, and revelation that really offer a sense of progression that makes Welcome to the N.H.K! and FLCL so timeless and enjoyable. I really hope that if you've seen one, you'll give the other a chance.
Tohru Honda is a compassionate girl who is down on her luck. Her mother having recently died, she has been forced to camp out in the woods for shelter. However, things start to turn around once she is invited to live with class hunk Yuki Sohma and his family... but all is not as it seems! Yuki's family is burdened with a dark curse which causes them to turn into the animals of the Chinese zodiac once hugged by a member of the opposite sex... and Honda may be the only one who can help them.
Yukino had it all. Brilliant, athletic, popular and pretty, she was the perfect school girl with many friends and admirers. But then one fateful day she met her match: a handsome young man named Arima. Now, not only is he beating her at her own game, she's becoming more and more dismayed to learn that she's developing her first real feelings of romance. Can Yukino maintain her model student appearance, or will love ruin all her plans?
I can think of very few anime that are as giftedly brilliant in their moments of comedy as they are also in handling their drama. Welcome to the NHK! is basically by far the best of these, but Kare Kano - despite the lack of an ending and unfortunate tendency to include massive recaps - is most definitely another. Each have elements of romance, though it is a much more major issue in Kare Kano, and both have elements of psychological introspection on behalf of the characters. Both of their soundtracks are really superb and sound very similar, too. While on the surface very different series I think they work for much of the same reasons.
Sawako Kuronuma is just like any other high school girl who wants to make friends and be useful. The only problem is she bears a worrying resemblance to Sadako from 'The Ring!' Because of her reputation, people are not only terrified of her, but small dogs even bark in fear at her presence; in fact, the only person in school who will talk to her is the lively class hottie, Kazehaya. As the pair spends more time together, Kazehaya slowly begins to bring Sawako out of her shell and soon their feelings for each other develop further. Though with her crippling insecurities, lack of social skills, and a series of cruel rumors and misunderstandings, it seems that Sawako's dream of a normal life won’t be quite so easy to obtain.
Both series feature loner or social outcast that slowly develops throughout the series to become more social and outgoing. Both feature a member of the opposite sex that helps that person come out of their shells. Both also have romantic themes that develop slowly, but take a backseat to the friendships that are created in the series.
If you liked either, you'll love the other. They are both filled with hilarious moments, moments that will make you tear up, and moments that will make you want to rip your hair out.