Looking for something with a strong plot. Can be shounen, seinen, or manhwa. Decent action is a plus, but plot is key. I generally like more serious series than those with uberhappy characters who shove friendship down your throat. On that note, main character can't be a complete incompetent that relies on his undeserved harem to achieve anything.

Superior - the plot gets weaker at the end, and the sequel is unfortunatelly not all that great, but as a whole it's worth reading.
Full Metal Alchemist

Shaman King
Rave
These two are my favourite action-adventure manga

Rurouni Kenshin
Samurai Deeper Kyo
Tsubasa: Reservoir Chronicle
these are all famous adventure manga

Magico maybe this is not really what you want, but I strongly recommend this
Double Arts if you don't mind rushed ending/axed, this is really good

i really enjoyed Kiss Wood and maybe you'll like Ludwig kakumei Its shoujo, but not that typical, i guess?

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I would try to buy the game versions of these as they are amazing games.

Tales of the Abyss - manga version not completed
Tales of Symphonia

Now for manga:

Erementar Gerad
Black Cat
Chrno Crusade
Mahou Tsukai Kurohime


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Being alone is only lonely if you want it to be.
Staying in lucid delusion for an eternity.

Before I forget further, I do have an answer for this thread: Kazan

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Kokou no Hito Best of best the plot is so unique and strong, the art is wonderfull the action makes your hear beat, the adventure is so good too and the protagonist is a lone wolf "modern" warrior im sure you will like this one ********

The Breaker It has a strong plot with little adventure and good action
Holyland This one got a strong plot the protagonist may seem lame at the beginning but it gets good and the action is one of the best i've seen

Fullmetal Alchemist

Black Cat.

Definitely seconding Kisswood.

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Go to work, send your kids to school;
Follow fashion, act normal;
Walk on the pavement, watch T.V.;
Save for retirement, obey the law.
Repeat after me: I am free.

Saver
One of the best manhwa I've ever read.

Vampire Juujikai (I don't know why it's not listed as adventure too, I think it is).
Shin Angyo Onshi

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What I like in Trivial Pursuit style. Pick your category: