Tamiko, Kinekuni and their son Inumaru live in an apartment in Japan and live a relatively slow and quiet life, until one day a beautiful girl named Maroko shows up at their door step. She proclaims herself as being from the future, and has traveled to the past to visit her distant relative: Inumaru, her grandfather. What follows is a wildly philosophical and intellectual journey: Tamiko storms out of the house, refusing to believe the whims of this new stranger; and Kinekuni and Inumaru invite her into their home. With spandex-clad time policemen after Maroko and the ethical dilemma of time travel at every turn, the Yomota’s will try their best to remain a family.
In a world where reality series are in high demand, an experiment was concocted: take regular folks who have dropped through the cracks in society, brainwash them to believe they are a real family, and see how they function as a family unit. The regular populace was so interested in the idea that this family was put in their own reality series, of course! Living in a closed environment and unaware of the outside world, this dysfunctional bunch do everything they can to remain sane... that is, until they accidentally escape!
Another strange anime about a dysfunctional family. Eternal Family is about a group of people on a reality show, and Gosenzo-sama is set up like a stage play (actors cheat out and gesticulate theatrically), so both have an interesting framing device unseen in most anime.
If you like your comedies weird and artsy check these out (though keep in mind Eternal Family is much much more spastic and zany).
When Utena Tenjou was very little her parents died, and a prince comforted her in her time of loss, giving her a ring with a rose seal. He so impressed her that she decided to become a prince herself one day. Now, Utena is a teenager at Ohtori Academy who's athletic and notorious for dressing in a boy's uniform. When a member of the Student Council humiliates a friend of hers Utena challenges him to a duel, and he accepts only when he sees she possesses a rose seal ring. She soon discovers that this is no normal duel - it's a bizarre and ritualistic battle that the Student Council regularly conducts. In fact when she wins, Utena finds to her considerable chagrin that she gets to have Anthy Himemiya, a rather docile student, as her 'Rose Bride'. If she wants to keep Anthy she'll have to win more duels against members of the Student Council and others. What is the ultimate purpose of these duels and Anthy's role as the Rose Bride?
Gosenzo-sama Banbanzai and Revolutionary Girl Utena are both highly metaphorical, existentialist works that try to subvert their narratives/genres. GB deconstructs itself using meta-references while Utena consciously exploits mahou shoujo devices to weave a new concept altogether. They're both surreal, revelatory, and brimming with humourous characters, and remind me strongly of each other.
From the depths of the human imagination comes Twilight Q, a Twilight Zone-style set of two tales based upon the paranormal and supernatural. In one story, Mayumi and Kiwako find a camera that supposedly came from the future, with very interesting film and already-taken pictures inside. Secondly, a tale by Mamoro Oshii which chronicles a strange occurance of planes turning into carp in mid-air, much to the dismay of private investigators and the media alike.
More of a recommendation from the second episode of Twilight Q, since both involve Mamoru Oshii, but they are also presented in a very similar way. They both have a very enclosed feel to them, mostly set within the same room for the whole episode, and the story is told in a very similar way by the characters.
If you like the way in which the story is told, the dark atmosphere and a story/situation that is interesting, you might like the other.