I have a thing for finished mangas, so in no order...
Blade of the Immortal - got a bit convoluted in the middle, but a great samurai story with supernatural elements
Kurozuka - a Korean version of "The Highlander," with superpowered immortals fighting from ancient Japan to the post apocalypse...what more can one ask?
Shin Angyo Onshi (Blade of the Phantom Master) - very similar to Berserk in many ways, heroes versus an empire run by demonic powers.
Ai Yori Aoshi - a fun and dramatic romantic dramedy, if you can get through it all, and it actually resolves the plots definitively!
Gantz - had its highs, its lows, and a passable yet "meh" ending. Still, a fun and grotesque scifi romp.
Elfen Lied - fun start, passable end, telekinetic catgirls fighting to the death...
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Now, on to the unfinished...
Rosario Vampire - admittedly, I dropped this b/c it got crazy, but I intend to pick it up again once finished. A fun supernatural harem comedy
Disciple Kenichi - similar as above, except with martial arts and no harem (2 primaries thus far)
Goldenboy - classic comedy entry, is this still going, is it finished? I don't know, but whenever I read it, I have fun with it
Till Death Do Us Part - a fun modern take on the traditional "Zatoichi" story (blind swordsman)
Attack on Titan - I have reservations as to how the story has progressed of late, but it remains compelling.
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Beautiful failures. The manga I want to like, are worth reading, but I got fed up with...
Air Gear and Tenjou Tenge - action mangas that ended, so there's that. But the back halves of both were weak.
Bleach - the never ending cycle of bullcrap, but it started out as a strong action manga
Berserk - Guts has yet to make headway in accomplishing either of his primary goals (restore Caska or kill Griffith) after nearly 20 years of story. As much as I once enjoyed this, I just don't have the patience to deal with all the waiting, just to see the author pour more salt on the wound. This has become torture porn in my eyes...
I'm sure there are others, but I can't think of any compelling ones offhand.