i'm a fan of what is called 'slice-of-life' anime and sometimes shoujo. animes of the slice-of-life genre usually follow the ordinary events of everyday life in an extraordinary way. here are some of my recommendations for an alternative anime experience...
kimi ga nozomu eien / the eternity you desire
kita e / diamond daydreams
you're under arrest!
kill me baby
pani poni dash
you're under arrest is a campy and lighthearted series centered around the everyday lives of two female police officers. the supporting cast is often zany, yet each character has his or her relatable moments. the voice actors of the english dub are inspired for the most part, especially the main characters. there are some exciting car chases and arrests that take place throughout the series, so it gets real once in awhile. the ~50 episodes of the first series are from the mid-90's, so the animation style and soundtrack might be a little dated for some tastes. i introduce you're under arrest to irl friends who are new to the slice-of-life genre or anime in general because there's a little something for everyone.