I will only drop a drama in pretty extreme cases, but in general I have a very hard time dropping things, esp dramas. I don't why, but I feel compelled to finish everything I start even when they're bugging me. Plus, there's usually some sort of incentive to continue: the hope that the show will get better, a certain character or characters, a particular storyline or if one of my favs has a role in it.
I have officially dropped only 1 drama so far & that was after months and months of trying to force myself to finish it. No matter how hard I tried though watching it was like torture so finally threw in the towel. There's another dropped drama on my list, but I know for sure I'll pick it back up in due course.
It's slightly easier for me to drop movies. It's weird because since movies are shorter I should be able to finish them, right? Nope, if they're boring me or something about it doesn't work for me, I'll drop it. But even so this rarely happens. Rarely. I just don't like not finishing what I've started so that makes me very careful about what I choose to watch.