Ok, so I like manga where the main protagonist is female. I like manga where the protagonist is strong, rather than weak. And I like manga with character growth. Now, a typical shojo manga, has either a girl protagonist that falls head over heels for some hot guy or a strong girl with bishie guys sticking to her like flies stick to honey. Neither is original or exciting to me. What I'd like to see is a manga where romance is not the focus, a manga that doesn't focus almost exclusively on what the heroine feels towards the cold bishie male lead (also an annoying personality, since pretty much every shojo manga with strong heroines has that kind of male lead - as if it's not possible to like any other kind of personality apart from a frost man in shining armor).

So, if you think you know a manga like that, I'd love to hear what you have to say!

Have you read Koi dano Ai dano? I think it might be what you're looking for as romance is not the focus.

Here's a couple more:
Six Half
Suki-tte Ii na yo
Kyou no Kira-kun
Hirunaka no Ryuusei
Dengeki Daisy

Ah...When I read your "likes," Oresama Teacher immediately came to mind. So if you haven't already, check it out. =]

Another shoujo manga that I feel deviates from the norm would be Tonari no Kaibutsu-kun. The main character is a physically weak study bug, but it's not like she's fawning over some strong savior guy.

Lastly, just some other mangas that I think are worth mentioning would be Akagami no Shirayukihime, Ao Haru Ride, and Bonnouji. However, I'm not entirely confident that those will suit your taste...But either way! Good luck with the search!

Have you considered looking at other genres? I have found that jousei and seinen have some pretty awesome stuff.

Shoujo:
Akagami no Shirayukihime - Kind of heavy on the romance, but still good
Basara
Return - Genderbender; There's someone who sticks like glue, but it's still good

Shounen:
Blood Alone

Jousei:
7 Seeds
Dokuhime
Kirai - Heavy on the romance
Ashita no Ousama
Heptagon
Udon no Onna

Seinen:
Otoyomegatari

Bitou Lollipop - one of the 2 shoujo manga I really like

Have you considered looking at other genres?

Ah, josei is fine too. By shojo manga I actually meant shojo/josei.

Thanks to all who responded! Honestly, I thought there will be recommendations with manga I have read everywhere, yet so far not even one title I read was mentioned 🙂

I second Six Half~
Cat Street- Both Cat Street and Six Half deal with the main girl lead trying to recover from what happened in their past (?). There's really nice character development, and as you wanted, romance is only a subplot to the stories.

Maybe...
Tomodachi no Hanashi- Well, this one is a bit different. Instead of the typical romantic plot, this one focuses nicely on the friendship of two different girls. It almost illustrates the definition of friendship. It's a refreshing read if you want something new. (Note: It kindaaaa has romance) 🙂

P.A. came immediately to mind
Barairo My Honey
Ten no Ryuu Chi no Sakura this.
Kimi ni Shika Kikoenai
Gokusen well, it isn't shoujo or josei but it's good 🙂
Chizumi & Fujiomi romance kind of is and kind of isn't the focus
From Far Away
Heart no ousama and Yuru Koi
Film Girl
Shiawase Kissa Sanchoume
Tenshi ja Nai!!
Shuukatsu!! - Kimi ni Naitei romance sort of is the focus, but also isn't
Beast Master
Nineteen, Twenty One
Please! Mr. Bear!
Mars has quite a bit of character growth
Skip Beat!
Liar x Liar definately
Usotsuki Lily
Love so life definately
360° Material romance kind of is the focus, but it's a nice read
Akatsuki no Yona I don't know whether it's got romance in it, but it's a good shoujo
V.B. Rose
Shounen Dolls
Meiji Hiiro Kitan
Shibariya Komachi
Honey Bitter

I am the master of my fate;
I am the captin of my soul.
William Ernest Henely

I rate manga with 5 being the average score.

just a short list of my fav shojo manga, all of them atypical:
Flower of Life
Heart of Thomas (yes BL is shojo)
From Eroica With Love
Hot Road
Banana Fish
Banana Bread Pudding
Basara
Moon Child
A Million Pound Love

[img]http://oi50.tinypic.com/1p7xj6.jpg[/img]

This list is exactly what I'm looking for! I just googled this, and this came as a search result!
I also like mangas where the characters developes in some sort of skill (showbiz, farsion, sports...), so I'll post some of them too:

Skip Beat - I'm guessing you've read this one, if not, do! This is my absolute favourite! About acting and showbiz.
Chihayafuru - About karuta (of all things). A traditional japanese card game.
Crimson Hero - Volleyball
1/2 prince
Seishunchuu

Akuma to Love song
Dengeki Daisy
Futago
Bitou lollipop
Girl in Heels - Weeeeird drawing style, but still quite cool.

Hiyokoi - Romance, and a shy main girl. But overload of cuteness, in a good way.
Kaichou wa Maid-sama
Kimi ga Uso o Tsuita
Yumemiru Taiyou
Papillon - Hana to Chou

The One - About fashion and modeling.[/m]
Akuma de Sourou
Beast master
Beauty Pop - About hairdressing.
Dance Subaru - About dancing. Pretty heavy, but cool.

Nana - This has suspense, and is soo good! But the mangaka is sick, and has been away from work for some years.. And it pains to not know the ending. So I'd wait with that one.
Gokinjo Monogatari - Same mangaka as Nana.
Lovely Complex
Nodame Cantabile - About music, and super awesome! But.. This should be watched (the anime is completed, and has wonderful music in it).
Paradise Kiss

Saruyama
Tokyo Crazy Paradise - Actually shounen, but same mangaka as Skip Beat, and it is quite cool! The drawing style is somewhat old fashioned in the first chapters, but the mangaka developes her style, and at the end it is more like Skip Beat.
Tonari no Kaibutsu-kun

That was a lot, but maybe you'll find it useful!; 🙂

I second Bitou Lollipop and The Secret of Friendship.
they are both lovely.