Off the top of my head, some manga I've dropped:
En Passant - while I liked the whole chess analogy, I had a hard time connecting with any of the characters, especially the main character. I think I made it almost half-way through the series (I've checked on it and found out where it finished at). Plus, I felt unconvinced by the direction the plot was taking - it just didn't feel well put together at all. And the relationships between the characters were not very believable to me either (like the girl liking such an unmotivated and negative main character who doesn't give a crap about anybody or anything, despite her sweet, innocent, and air-headed disposition).
Cage of Eden - I made it through over 30 chapters, but apart from the cool mystery solving sequence where the main character watches the video and learns what happened to the people who had still been on the plane, I just felt like head-desking the rest of the time. Akira's best friend's character felt like it went really out of character and unrealistic to me when he decided that murder was ok (one person as an accident, fine, another person out of paranoia, maybe, but his thoughts after that were too much of a stretch for me). And while I'm ok with a little ecchi in usually a humourous context, the number of fanservice panty shots just added to my desire to drop the series. Having the know-it-all come up with answers so readily all the time is so cop-out, it feels like reading a mary sue (or gary stu). It doesn't feel properly researched (although some aspects do, the overall story is just lacking in good plot development that blends fantasy with fact) (actually, even just good plot development as a story feels amiss).
Hwang Mi Ri and Han Yu-Rang stories that I haven't already completed. Why have I decided to drop these authors altogether (and never pick up another one of their stories)? Their main characters are practically carbon copies of one another (especially the main male in his character design and personality and abilities, and the female in her personality and abilities and relationships with other people). It's hard to believe the depth of feelings between the two main characters (she loves him sooo much... but there's really no connection on a personality level it's all in just the looks) (she usually has more of a connection with the second-place guy who actually develops a potential romance with her on more than just looks). The plot usually starts off so interesting and different, yet by the end of the story, it has the exact same outcome as all the others, and certain plot points that always happen you can pretty much predict the entire thing. And while there may be moments of possible foreshadowing, those are pretty much forgotten along the way (the plot jumps from moment to moment like a person's thoughts scattering here and there, and there's no overall flow or connection from beginning to end). Really you can't think too deeply about these stories since there is no deep thought put into them, just take it at face value. If you like to think about stories in depth, you'll be highly disappointed with these ones.