Well, most animes shown on MSM are, you are right, unfortunately just generic shows revolving around fighting. But that's because the Western World hasn't picked up most of the stuff over there, or most of it has outsourced itself to the depths of teh internetz anyway.
There are many great anime for adults, more or less known. With that I don't mean funny porno crap, but dark, atmospheric stuff. So @topic, personally I can recommend:
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Death Note: Dude finds a note allowing you to kill people by just writing their name in it.
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Berserk: Set in a European Medieval inspired fantasy world. Lots of blood, gore and betrayal.
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Hellsing Ultimate: Nazi Vampires!
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Naoki Urasawa's Monster: Master chirurgeon saves someone from an otherwise fatal bullet wound. Problem: This someone is a notorious psychopathic serial killer. (my current avatar is from there. Mr. Grimmer is a great character)
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Animatrix: Origin stories of 'Matrix'. Amazing atmosphere.
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Ergo Proxy: Post apocalyptic future stuff; amazing atmosphere
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Ghost in the Shell series: Cyberpunk detective story
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Mardock Scramble: Just some meh revenge story, but the unique art style is marvelous, and the philosophical aspect is great.
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Afro Samurai: Dito. No philosophy, but instead features Samuel L. Jackson as a voice actor.
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Elfen Lied: Some mutant girls with super powers used for experimental testing. Quite messed up. Perhaps too messed up.