Not all anime is deranged wildness and excess. In fact, some of the best shows out there focus on real life as lived one day at a time, with only occasional excursions into the outlandish and outrageous. Here's some of the best, listed in alphabetical order.
In many ways this anime (and its predecessor manga) set the template for a whole subgenre of slice-of-life anime: the Gang of Schoolgirls Doing Things Together. The six girls of a certain high school class and their (unmarried, still rather adolescent herself) teacher serve as the starting point for any number of hilariously weird observations about the strangeness of everyday life. (Most consistently hilarious is space-case Osaka's fantasy ideas about Chiyo's braids.) Other shows have copied the formula, but none of them got it quite as right as this, in big part thanks to the way both broad humor and careful observation of character work together.
2. Bunny Drop
A thirtyish wage drone's life is upended when his grandfather dies and leaves behind, not a fortune to be divided, but a six-year-old daughter, Rin, whom he apparently sired with his housemaid. No one wants to care for the girl, so our hero steps in and discovers that bringing up a daughter in the modern world is a good deal more complex and nuanced than he imagined. That and he's determined to find out the truth behind Rin's alienated mother, even if it means digging into things best left alone.
Aside from being a deeply affecting story, told without gimmicks or pretense, this is also a beautifully presented one, animated in the pastel hues of a watercolor come to life.
One of the rules of this list is "nothing outlandish," so you might wonder why the deliberately outlandish FLCL is here. This is, after all, a show where one of the plotlines is what's up with those aliens that are popping out of the protagonist's forehead after he's clobbered with a bass guitar by a Vespa-riding girl who moves in with his family. Yes. But the tone of the show, despite the absolutely outlandish goings-on -- it was from the same creative team as Neon Genesis Evangelion, so expecting it to be anything other than berserk is probably naïve -- is strongly rooted in the ingredients of everyday life, so it deserves mention here.
Many anime have references in the story, either sidelong or head-on, to anime fandom itself, but Genshiken is about anime fandom -- specifically, the misadventures of a college anime fanclub who bring in some new members, not all of whom automatically know anything about anime to begin with. This last touch makes the show somewhat more accessible to non-fans, especially thanks to the easygoing, prescient and observant way the show is constructed -- there's little of an overarching plot, but rather just a succession of experiences that more or less lead into each other.
"Greenwood" (sometimes "Green Wood") is the name of a boy's dorm at the Ryokuto Academy, where harried student Kazuya Hasukawa tries to settle in and make the best of being surrounded by one rather kooky fellow student after another. He opted for dorm life over staying at home to put some distance between himself and his brother, but now he's got a whole new slew of problems to deal with. This isn't a groundbreaker of a series -- it's adapted from a girl's comic that ran in the 80s and 90s, and it's wildly melodramatic at times -- but it's fun to watch, and even mocks its own plot holes when things don't make too much sense.
After Azumanga Daioh came K-ON!, more or less -- the saga of a gaggle of girls who form a band as an after-school activity, but are really just looking for an excuse to hang out and do stuff together. It has the same mostly plotless storyline; it's really about the various girls' personalities as they make their way through the school year, make music, and make each others' lives that much more enjoyable.
8. Kids on the Slope
A young man -- a skilled piano player who detests jazz -- ends up in an impromptu jazz band where the local school's tough guy is the drummer. This love letter to both jazz and being a kid in the 1960s is a masterwork of its kind -- the sort of show where the individual ingredients don't seem extraordinary, but the way they're put together is somehow transcendent. It also perfectly captures the sunny, afterschool feeling of young adulthood, when everything seems possible if also only just out of reach.
Her real name is Sawako, but everyone calls her "Sadako" (a reference to the horror movie The Ring) both because of her appearance and her generally reticent nature. Then she begins to bloom under the guidance of two other girls who are as outgoing and brassy as she is not, and who guide her towards the one boy who stands the best chance of making her really flower. Not just a good story, but a good-hearted one.
10. Lucky ☆ Star
Another, and most likely iconic, version of the Girls Doing Stuff Together subgenre, and also one of the best thanks to its flip and irreverent tone. Of the four girls who make up the main cast, our attention is dominated mostly by the slacker / gamer / wiseacre Konata Izumi, whose every other utterance is a quotable line, much to the amusement or chagrin of the other three. The breaking-of-the-fourth-wall segment at the end of every episode is a hoot, too.