So many people have said that this anime, like Seinfeld, is a show about nothing. I think that viewpoint misses something. Azumanga Daioh may not have a sustained story arc, or a grand destination in mind, but watching it reminded me of my own days as a high-school student.
Be it Chiyo wishing that people would stop treating her like a kid, or Tomo acting every bit a fool and enjoying every minute of it, or Sakaki being uncomfortable with her towering stature, or Yomi's constant concerns about her weight, or even Osaka's frequent non-sequiters, this is a series about growing up with your friends.
And the characters are all truely likeable, as well. Even those who can be seen as annoying at times can't really be faulted for their personality quirks.
The series is fun and heartfelt.