These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Azumanga Daioh
Awesome Music: The opening and closing themes, as well as many of the image songs. In particular, Kagura's "Ashita wa Makenai! GO! FRIEND!" and Sakaki's "Kokoro wa Shoujo de PARACHUTE".
Base Breaker: Depending on who you ask, Tomo is either considered to be one of the funniest or one of the most annoying characters in the series.
If you can listen to Soramimi Cake (aka "Mondegreen Cake") without it getting it stuck in your head, you are officially immune to any Ear Worm.
Also, there's E'ye or E'ye 2; the songs used for the eye-catchers during the commercial breaks? If that tune doesn't turn into a ringtone for your cell phone, then you officially are deaf to any and all Ear Worm.
"Funny Aneurysm" Moment: There's a joke in the supplementary lessons about Osaka thinking it will be a good day because she woke up early, only for an earthquake to rock the school a moment later. By the way, the school is in Tokyo.
Het Is Ew: The fact that the cast is all female, minus two recurring male characters (one of whom is a perverted teacher with a thing for highschool girls, and the other being an imaginary cat creature... maybe), might leave some viewers with this impression.
Mary Sue: Could be a deliberate subversion with Sakaki: she's tall, beautiful and athletic, intelligent and educated, is kind and polite and has a wonderful singing voice and may or may not be rich. Except she doesn't want any of this, she just wants to be small and cute and tend to cats, but all cats everywhere well, mostly anyway seem to instinctively attack her viciously. And the wounds she gets from those attacks, combined with her calm demeanor and her physical size make her seem to other students more like a scary delinquent than anything. Or, in case they don't think she's a delinquent, they admire her beauty and athleticism from afar and never approach her.
Moe: The series itself is something you can curl up with, but Chiyo-chan is Moe to the nth degree (especiallywhen she's in the penguin suit), and Osaka and Kaorin are also incredibly cute. Osaka may actually be at least partially responsible for the popularization of the concept, placing second in the 2002 Saimoe Tournament.
This series is sort of proto-moe itself, once you think about it. It codified a lot of tropes related to the "genre".
Superlative Dubbing: While fans give the English dub mixed to positive reviews, most official reviews don't hesitate to compliment the dub cast, and they do deserve props for getting just about every cultural reference across to Western viewers quite well.
Values Dissonance: Sakaki's lack of self-esteem, especially when comparing herself to Chiyo, seems downright ludicrous to western viewers who don't understand the difference between Japanese standards of beauty and their own.
You may feel sorry for Chiyo after all the abuse she cops from the two resident jerkasses, and how she sometimes has trouble being taken seriously due to being much younger than her classmates.
Animals seem to have it in for Sakaki despite the fact that she adores them; her woobieness is rarely so highlighted as the time she lets Kamineko sink its fangs into her hand... and Sakaki doesn't pull her hand away so that she can finally pet him with the other one.
Also noteworthy is the attempts Sakaki's friends make to please her. They try to be friendly and warm to her, but unintentionally end up hurting her feelings. Kagura is particularly guilty of this when the two first meet.
It's hard not to feel for Osaka's inability to stay focused, let alone succeed sometimes.
Kimura's after Kaorin, much to her despair. You can't NOT feel bad for her, even though it's funny.
Iron Woobie: No matter how hard the world tramples on her, Sakaki never gives up trying to be a good person.
Episode 2 has Osaka deliver a pun: "That's not bean knowledge (a Japanese idiom meaning "trivia"), it's knowledge about beans." In the dub, it's changed to "That ain't no grain of truth, that's the truth about grain."