At the beginning I watched everything till the bitter end, later I just dropped, now I skip episodes if the Drama has any aspects or characters I like.
i just watch the first few eps, if i still dont like it i just drop it n start ranting about how shtty the drama is to my friends XD 
i have forced myself through a couple of dramas HOPING that it gets better - storylines picks up pace or the actress (which it normally ALWAYS is) gets less annoying. Sometimes if the storyline is good enough but the actress isn't too annoying I can live through it but if it's a combination of annoying, clingy, whingy, nosy and bad acting I just drop it. Now I have a 3 Max Rule that I go by so I don't waste too much time on dramas that I don't like by forcing myself. Sometimes even 1 episode is enough to tell me if I'm gonna enjoy it or not but the majority of the time it takes up to 3. 
I really don't like to drop dramas but when they're unbearable I drop them... usually I try to finish them as soon as possible tho
I drop it. If I'm that curious how it'll end up, I just google it Lol
I usually drop them but sometimes there's this nagging feeling inside me that makes me want to know how it ends even though I get bored in the middle part or 3/4 of the story. I keep on thinking, maybe they'd somehow save the show. But as Bae said, I also drop it when it's unbearable to watch.
For me if I don't get hooked on the drama within the first few episodes then I drop it but a couple times people have been like "omg u haven't got to the good part" so i watch like 10/16 episodes and then drop it. I swear it always gets so boring like 3/4 of the way through and i'm impatient lmao
If I don't like a drama, I drop it. Life is too short for bad/boring dramas!
I used to force myself to finish dramas I hated until Dream High 2 happened and I just couldn't. I loved the original and I really couldn't with the sequel.
I used to make myself finish them, but then I realized how it leaves a terrible "aftertaste" and I feel like I've wasted too much time on the dramas, so I just drop them now. 
My on-hold list is basically my dropped list - there are a bunch of 1/XX episodes where I just watched and thought "yeah this show is not targeted to me and I don't enjoy it" and then there is another grouping where I watched to about the halfway mark (maybe a bit further) and stopped because of a twist or I could feel a massive dropoff.

Generally I do finish dramas I start because I am interested in how they are going to end. I'm generally pretty open to watching anything and I don't start many dramas if the summary sounds like I wouldn't enjoy it.
I usually don't drop a drama once I start watching. It would have to be reallllll bad and boring. What I do is I skip a lot and look for the parts that interest me. I used to ask how could these things be so silly but then I reminded myself that they are just dramas. What is a drama without some trumped up story to create ... .  Drama!
depends really because i usually drop it during the first ep if it doesn't catch my attention (tho i usually wont add it to my acc since i didnt even finish that ep) but i can also pull through for a few eps. with healer, i didn't really get into it til ep 5-6 but im happy i continued that
I finish them (lots of time with skip watching or skimming through it) if I'm watching them for a particular actor or actress I like, I'll watch their scenes and complete it at least like that - but if it has no actors I like or I'm not curious about anything, then I'll drop it for sure lol
If the acting is worth it I will watch it anyway even if the story is a joke or low budget.