There's a bunch of teacher/student romance out there. Not so much teacher/student friendship (or so I think). I'll take any genre. It can be either a teacher making friends with the whole class, or a single person/group making a close friendship with the teacher although I prefer the latter. Thanks in advance!

Examples I've Read:
Azumanga Daioh - the main group's relationship with Yukari and Nyamo
Gokusen - Yankumi and her students (as long as I ignore the 2008 SP manga)

GTO?

Tried reading GTO a few months back. Couldn't really get into it all that much. I might go back and give it a second chance though if people really recommend it.

Cat Street - El Liston principal
Flower of Life - literature teacher
Nodame Cantabile - "Milky"

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Avatar by tassyn.livejournal.com

Reading: Kingdom, Sangokushi, Historie

Hana Kimi: friendship between heroine and gay school nurse

Kimi ni Todoke: There's a teacher who always ends up hanging out with the main group of friends.

Sket Dance: this is kind of stretching it, the story sometimes involves the teachers in hilarious ways. just read it.

I really really recommend it.
Though for what you asked, maybe the live action is better.

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What I like in Trivial Pursuit style. Pick your category:

isecond GTO but it has little or none romance


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<b>Reading</b> <!--m_gen--><a href='http://www.mangaupdates.com/series.html?id=1859' title="Click for series info"><u>Love Lucky</u></a><!--m_gen_end--><BR><b>Recommended</b> <!--m_gen--><a href='http://www.mangaupdates.com/series.html?id=5920' title="Click for series info"><u>B Gata H Kei</u></a><!--m_gen_end--> <3 <!--m_gen--><a href='http://www.mangaupdates.com/series.html?id=24665' title="Click for series info"><u>Conveni-N</u></a><!--m_gen_end--> XD<BR><!--img--><img src='http://myanimelist.net/signature/chulian1819.png' border='0' alt='User Posted Image'><!--img_end-->

In "Crossroad" ( http://www.mangaupdates.com/series.html?id=5750 there's an interesting relationship between the female protagonist and a calligraphy teacher / school counsellor.