A ton. I'll just name a couple of the more notable ones.
Reborn: The series had a spark but it's absolute trash now. I tried getting back into it a couple months back but it got even more terrible.Easily the worst Jump manga out now. I just couldn't take the assyness anymore.
Bakuman: It got too repetitive for my taste. IMO, it should've ended a while ago. The writers are just extending the inevitable end at this point.
Naruto.. I am just done.. just done..
Dropped Bleach, but I picked it back up begrudgingly..
D.Gray Man. Should have ended after the Noah arc.
I am sure there are others I can't think of at the moment.
Kill Me Baby. Granted I only watched two episodes before I dropped it, which is hardly half. I was expecting hilarity, and I got non-hilarity (Sure, the bear thing made me chuckle at first, but they drew it out far too long!)
Boku wa Tomodachi ga Sukunai- I was hoping the story could drown out the ecchi, but I got to the pool bit of episode two and Booberella's boobs just got annoying.
Those are the only two that are notable. I've never really dropped a series halfway in, it's normally right near the beginning or else I'm all "Well, I wasted this much time, I might as well finish it..."
I dropped both the manga and anime of One Piece and the anime Naruto... mainly because it became so damn repetitive that I couldn't stand it anymore, that and I was growing out of anime pretty much... Inuyasha was another anime that I stopped watching as well.