Azumanga, being the seminal manga, produced an enormous number of imitations and cameos.  Usually it's something small, like Chiyo-chichi on a fan in Love Hina.  In Ichigo Mashimaro, Chiyo-chichi and Yotsuba meet the main cast outright (and Chiyo-chichi says "I am Azuma"). 

The anime prompted some of that as well.  Here's a little cameo in Happy Lesson:

Azumanga's creators did it too:

I wish someone told me what they referred... In this case, we can be reasonably sure that it is, indeed, a cameo (unless it's just a joke designed to make fans to crack their heads guessing).  But I know a trickier case. 

In Chobits, a sizeable chunk of the action happens in a bakery called "Tirol".  This is how its sign looks:

The sign says "欧風菓子 チロル" (oufuu kashi chiroru, European Sweets "Tirol").  Now, in ep.24 of Azumanga they have a Tirol too!  It's even shown twice, by night and by day:

Here's the signage, enlarged:

It's a little blurry, but it clearly says "手作りお菓子 チロル" (tezukuri okashi chiroru, Handmade Sweets "Tirol").  Is this a reference to Chobits? 

I honestly do not know.  Chobits and Azumanga Daioh were broadcast in the same season (which begs the question just how Rie Tanaka managed to do lead roles in both!).  Tirol appears in Chobits ep.8, which gives about three months or so to insert the reference into Azumanga ep.24.  It is possible.  And it's too much of coincidence.  But for a purposeful reference, it's too timid.