Azumanga Daioh is my favourite.

True, it's not the funniest anime out there. But there's so much more to it that just comedy. I like to think of it as:

ONE THIRD hilarity ("If you get lost, gather round Sakaki-chan!")
ONE THIRD weirdness (most of it in the New Year's Dreams episode)
ONE THIRD cuteness (Sakaki playing with Mayaa. "Meow." "Haaah!")

I've read the manga and, yes I've compared it with the anime. The manga has a few more dirty jokes (directed mostly at Sakaki's breasts)but the anime has some golden moments (Osaka feeding Penguin Chiyo)so I guess it evens itself out pretty well. But I still mourn over certain parts that the anime left out that were just so funny in the manga, like Tomo and Osaka's practice for the 'univeristy interview'. "I pounded in a wedge once!" "Good you pass!"

But the Mayaa + Sakaki <3....Couldn't imagine it being done any better.