I really like how lots of people in this thread just post whatever anime they like best and ignore the OP's request for anime similar in the style of azumanga daioh, lucky star and Haruhi Suzumiya.
Of course this is not saying that all the suggestion are bad, since that's a matter of personal taste. But I think one should always be aware that personal tastes are different among people, and should always make his suggestion with the other person's taste in mind, a trait that's lacking among people in general.
To OP: Like many people in the thread said, K-On is probably the closest to lucky star and azumanga daioh. School Rumble is also decent and similar in style. As of Haruhi Suzumiya, it really depend on what part of it you like better (Personally I found the character annoying). If you like the director's style look for his other work (Clannad, Fushingi Yuuhi, Kanon) If you like the sci fi angle maybe To aru majitsu no idex. If you just like the style of light novel adaptation there's a whole bunch of anime out there for you to try (most of them not good in my opinion).