The school/training center doesn't have to be the main plot.

I've already read or looked through the following:

Shade: The Other Side of Light
Freezing
Senki Senki Momotama
Zero
Mahouka Koukou no Rettousei
Black Haze
Crepuscule
Trump

Rosario to Vampire (mc is a normal human who goes to a school for monsters)
Beelzebub (mc becomes the adopted father of a demon)
Special Martial Arts Extreme Hell Private High School
Dragons Rioting (this is an ecchi manga but it fits your criteria)
The God of High School (this is epic)

psychic academy

[img]http://www.nodiatis.com/pub/19.jpg[/img]
[img]http://www.dragonflycave.com/wpay/alakazam.gif[/img]

Hidan no Aria mercs
IS exosuit pilots
Gun X Clover mercs
Ichiban Ushiro no Daimaou magic
Kikou Shoujo wa Kizutsukanai puppeteers
Zero no Tsukaima magic
Kurogane Hime haven't read it
Magikano magic school doesn't show up until later
Tokyo Ravens magic/spirit
Tora Kiss - A School Odyssey magic/battle/avatar?
Witchcraft Works magic, sorta
Mahou Sensei Negima! magic

How come nobody has said ANSATSU KYOUSHITSU

Live for something otherwise u'll die for nothing

seconding ansatsu kyoushitsu, ITS AMAZING!!

[img]http://24.media.tumblr.com/216cc00f39657290be4449181192559d/tumblr_mrmmn3Swm41sfaak1o1_400.png[/img]

It's rather Ecchi but try Kanokon

Beware the Fox, for while he is wise, he is also mischievous and cunning!
[img]http://puu.sh/dn6tb/f47075ed31.png[/img]

Quote from sunder

Hidan no Aria mercs
IS exosuit pilots
Gun X Clover mercs
Ichiban Ushiro no Daimaou magic
Kikou Shoujo wa Kizutsukanai puppeteers
Zero no Tsukaima magic
Kurogane Hime haven't read it
Magikano magic school doesn't show up until later
Tokyo Ravens magic/spirit
Tora Kiss - A School Odyssey magic/battle/ ...

Agreed on all these, plus you could read or try:
Arachnid
Aphorism
To Aru Majutsu no Index // To Aru Kagaku no Railgun
Trinity Seven: 7-Nin no Mahoutsukai
Tripeace

"Spread your ear-pollution both far and wide" - Billy Squier, The Stroke.

Flow fits perfectly.

Ciel
Animal Academy
Gakuen Alice
Love Monster

Favorite Art:
Oboreru Knife
19 Days
Gangsta