What about Wolf's Rain?                     
There 4 wolves searching for paradise , while Earth is near to the end.  Wolves are named : Kiba , Tsume , Toboe & Hige . Soon a wolf - dog , Blue joins them.  Those animals have mastered the illusions that make them look and sound like human.  As the old legend says : ,,Only wolves will know how to find paradise."  On their journey , they face  so many dangerous situations , meet new enemys and friends. But they don't have much time left , 'cause Darcia wants to open paradise.  In the final episode Kiba fights against Darcia , defeats him and brings the normal life to the world.                                                                                                                                                                                                          

My all time favorite is Ayashi no Ceres. Dunno if it would be your speed, but I would check it out.

If you're looking for something kinda crazy, take a look at Is This a Zombie?

If you are looking for a cool art style and some amazing action and animation, check out Bakumatsu Kikansetsu Irohanihoheto (That one is hard to type ).
This is probably the most amazing animation I have ever seen...

And finally, Ghost in the Shell...basically all of them.
Ghost in the Shell (the original movie) has some beautiful art, a great story (lots of deep psychological themes...gotta watch it more than once to really take everything in.)

I would suggest an anime/cartoon hybrid called RWBY from Rooster Teeth. It is made in the USA, so it is fully English. They may be in a school, but it is more of a college for fighting, and doesn't have that much fan service except for one character, who really you can't consider fan service that much. It has a unique art style, and it is in its 3rd Season, currently on its 6th Episodes. Seasons usually run about 12 Episodes, and they have little background episodes to tell you about some of the technology and naturally occurring things of its world. Hope you check it out.

emptysenji :   Any of the Ikkitousen shows were really good, but fan service is there, and it is kind of a school show, but the heads of the school take on the identities of the old Japanese warlords, and the rival schools fight each other for dominance.  I would highly recommend Jormungand and Berserk if you like bloody, like Hellsing.  Elfenleid is another good one as was the first Ghost in the Shell movie.  I am currently watching Seiken no Blacksmith, and it is pretty good so far.  Claymore was a really good one if you are into the fantasy thing with swords and lots of fighting

I would recommend Clannad to anybody looking to start getting into Anime. It was the first one that I managed to watch in Japanese sub and wow, it is possibly the best choice I could have ever made. It seriously features some of the best characters I have still been able to find in an anime so far, (I mean I have only watched about 50 so its not the greatest sample size ever but still) the two main characters are developed brilliantly, as separate people and together as a couple. The supporting characters also get there own episodes decidcated to them which really gives them characters as well. The second season is even better as it explores how life really is outside of school as well as giving the main couple more development as they deal with adulthood. And god, the ending, I'm not going to spoil it but it is one of the most emotional things I have ever seen. Seriously, everyone who is reading this, go ahead and watch this. It is not one of the most highly rated shows for no reason.

And I was 13 when I watched this so OP should be able to get through with this no problem.

Ok, here's just a few I've seen and enjoyed enough to recommend (you make it easy because we have the same taste)

Steins;Gate
Claymore
Attack on Titan (only one season so far, 25 ep)
Sword Art Online (you can only watch the first half and wont miss anything)
Jormungand (very similar style and world as Black Lagoon)
Deadman Wonderland (although the anime never finishes the story)
Future Diary (omg so unique and brilliant)
Baccano!
Durarara!!
Psycho-Pass
Cowboy Bebop
Black Butler
Samurai Champloo
K   (yes that is the entire name)
Blood Lad
Code Geass (people either love or hate this one lol)
The Heroic Legend of Arslan (2015 remake)
Two girls, one cup (ha ha just kidding)
Fate/Zero
No Game No Life
The Legend of the Legendary Heroes
Darker Than Black: Gemini of the Meteor (they made a second season for it  )
Trinity Blood
Akame Ga Kill
Devil May Cry (they did a lot better on this than you would think imo)
Parasyte: The Maxim
Tokyo Ghoul
Witch Hunter Robin
Phantom : Requiem for the Phantom
Soul Eater (maybe a little too kid-y for your taste)
Outlaw Star (one of the gems of my childhood)
Speed Grapher (never seen it, heard good things)
Gargantia on the Verdurous Planet
Yu Yu Hakusho
Fooly Cooly (also written as FLCL)
Ergo Proxy
Wolf's Rain (I didn't care for this one, but many people love it)
Basilisk
High School DxD (there is MASS fan service here, but i still found it watchable for the action)
Samurai 7
Monster (very slow paced, but a damn good story)
GunGrave (never seen it, heard good things)
xxxHolic (never seen it, heard good things)
Jyu Oh Sei (never seen it, heard good things)