Can you give me a timeframe? And a more firm defintion of mature.

Are you talking dark and gritty or just seinen/josei?

Anything that doesn't revolve around little kids with magic powers saving the world

I hate these cheesy anime cliches like this one:

#1 Villain wants to take over world
#2 Hero doesn't care about anything, he just wants to protect female lead
#3 Hero does something "impossible" (absorbs a spell)
#4 Hero slices Fireball with a swrd
#5 Talking sword
#6 The line "I won't forgive anyone who hurts..."
#7 Hero gets beaten by villain and then powers up to one shot the villain
#8 Ends with a Slash showdown type effect
#9 Somehow powering up allows the sword to change
#10 Hero yells villains name as he destroys him
#11 Hero is a normal high school Japanese boy with normal hair
#12 Female lead is a girl that has an unnatural hair color (pink)

I like anime that revolves around worldy issues, like Wings of Honneamise, here is a quick review of WoH:

Two rival nations are vying for political and military dominance. The much ridiculed fledgling space program becomes a pawn in this power struggle as one nation tries to use it as a propaganda tool and bait to lure its rival into war. No one expects a real, working rocket ship to be created.

At the center of the conflict is the brave, volunteer test pilot, who is transformed overnight from an air-force reject to the symbol of the new era. His physical ordeal of surviving the rigors of flight training, not to mention the assassination attempts, becomes secondary to his attempts to justify the vast resources expended on the project while people are living in poverty just outside the training center.

Finally, all worldly issues are transcended as the rocket actually lifts off (with stunning animation), much to the amazement of the troops fighting over its possession.

Have you seen Puella Magi Madoka Magica? Watch the whole thing all at once, and quickly learn that things are not as they appear, no matter how cutesy on the surface.

As I kinda thought, you're not really looking for 'mature' anime in the sense of universal terms. If that were so, I'd had a ton of josei to show (Princess Jellyfish, Nodame Cantabile, Usagi Drop, Sakamichi no Apollon, and NANA), but you're looking more action shows with grit and story which means I'd have to leave out gems such as Trapeze, Planetes, Tatami Galaxy, Space Bros, Arakawa Under the Bridge, Intial D, Hotarubi no Mori e, and Giant Killing.

To fit more to what you're looking for, I'd say things like Baccano!, Hellsing Ultimate, Fate/Zero, Mononoke, Rainbow, and Black Lagoon. There's also more mature things like Kaiji, Akagi, Steins;Gate, Tiger and Bunny (kind of a stretch here but it's good), Kara no Kyoukai, Natsume Yuujinchou, Madoka, Katanagatari, Bakemonogatari and Nisemonogatari, and finally something like Redline is a good finish.

EDIT: I'll bold names for you since there's so many.

Yeah, Turkish should definately watch Madoka... all of it...

It looks really childish, but I'm willing to give it a chance due to the fact that it has a very high ranking on MAL and people recommened Steins;Gate to it, wich I liked very much.

Thanks for recommending those shows, I'll look into them, altough I watched most of the shows in your 2nd list. Someone recommended me Planetes after WoH. Does Usagi Drop have a similar feel like Natsume?

I was away from anime for a couple weeks because I was busy watching the first season of My Little Pony to see what the fuss was about. I'm glad to report that I'm back to my senses and ready to go back to watching good ol' fashion anime. Though Rarity will always hold a special place in my heart.

I need to finish "Monster" I have like 12 episodes left and I haven't watched it in weeks!

It's pretty ok, and I can understand why people fall so hard for it, the main six characters (Ponies) are extremely likeable, even loveable. You get attached to them way too easily. That said, it's that attachment that blinds you from ever criticizing the lousy parts/episodes of the show.

Also the fans can be pretty creepy and I don't want to be associated to them.

As for monster, It started losing steam somewhere between episodes 40 and 50. It started off wonderful, and I would watch 4 or 5 consecutive episodes in one sitting. However it started to become predictable and even boring somewhere down the line. The mystery and drama elements that made it so good vanished. I will finish it though.

All of those are 'mature' show that have been released in the past year or so (with the exception of Baccano and akagi/kaiji).

Usagi Drop isn't like Natsume at all. Usagi Drop is a pretty unique show and while I can compare it to other manga, no anime comes to mind (except for Aishiteruze Baby which isn't a good comparison).