Yes, but it's has to be pretty rough for me to such as.. Over dramatics like when you watch a melodrama and the mother-n-law screams all the time. I can't take it. I like drama, but when every one of the characters are screaming every couple of seconds I drop it. When the drama goes in circles for about 85% of the drama I drop it. When no one can pull me into the story line by the 10th episode and I give it to the 10th episode. With the 10 episode method it's where the story line makes no since and the acting is really really bad. Other than these I can hold out but I will drop if its bad. 
No. I don't have the amount of free time anymore, nor do I have the patience, required to finish a drama I'm not into at all. I'll give it a few episodes but I'll drop the ones I'm not that into nowadays.

Movies sometimes I finish, sometimes not, depending on how much I dislike it and whether I'm watching it alone or not.
I can't drop a drama. I"m not particularly sure why except that I hate the feeling of not finishing something and my curiosity. I need to see how it will finish even if I hate it. I don't want to miss out on even one scene I might end up loving. Most of the times, the dramas I dislike are ones other people adore and I almost feel obligated to finish the drama just so I can fully explain why I DISLIKED it. There's nothing wrong with someone explaining why they dropped a drama, but I do get annoyed when people bash a drama they only watched one or two episodes of. It's fine to say what you didn't like, but it gets obnoxious when they dismiss and then bash the entire drama out of hand so early on. There is nothing wrong with speeding through a drama I really hate though. haha 

i drop the drama when i know that i'll always sleep sometime while watching it. 
when i realize that just the first episodes are boring and starts getting some action into it, i keep watching till the end. 
something like this