A couple of weeks ago, I ordered a copy of Azumanga Daioh #1, to see what it was like. The draughtsmanship instantly struck me as exquisite, but the stories (it uses a 4-panel approach) were a bit hit-and-miss to begin with. Then, I came across this one, and realised we had something special here (read dialogue right-to-left, by the way):
By half-way through the book, it was clear that this had real potential, so I ordered the other 3 books in the series. New characters were being introduced who had real personalities, weren't just stereotypes, and who you (well, I) actually began to like and care for. What's more, in places it was very funny — sometimes in the picture or with slapstick, but mainly through knowing the characters. This, for example, isn't really funny at all unless you know what the character in glasses (Yomi) is thinking:
The series concerns the progress of six girls through their final years of school, ending with their university entrance examination results. That's why it ends: unlike Peanuts (which I adore, and with which it is sometimes compared), the characters do get older and do change over time. After I finished reading it, I re-read all four volumes straight through all over — something I haven't done since The Lord of the Rings (well, unless you count the TOPS-10 Monitor Calls manuals).
My daughters like it too. We spent two 30-minute car journeys talking about it. So strong was their conviction of its goodness, they even managed to persuade my manga-fearing wife to read it, too (she's currently half way through volume 1 — just about where it starts to pick up).
If you don't generally like manga, but do like clever, character-driven tales of innocence and whimsy, go for it. If you do like manga, you should have it already.