Excel Saga (and it's little side show: PuniPuni Poemy)
and I'm surprised no one mentioned Masaru (or Sexy Commando Gaiden Sugoiyo Masaru-san!)
both are like stupid funny, I almost choked laughing watching these

as for Azumanga, these were actually a series of newpaper mangas, it spans the four years of high school in Japan, it's like a classroom comedy, really light hearted... I don't know how they did the series but the mangas are really funny...
some of the characters are:
Yukari - homeroom/English teacher
Chiyo, Tomo, Sakaki, Yomi, Osaka (not her real name, real name is Ayumu Kasuga)... there's a couple more characters that add on later...
It's difficult to explain, but the manga was worth reading....