If I've invested my time in more or almost half of the drama already, I usually read recaps for the rest of the episodes  if I can't bring myself to watch it.
However, if I've watched episode 1-3 and I still don't like it~ I drop it. 
Well, I finish what I start no matter how hard I have to force myself to do so (not only drama related). 
Only sometimes, but if it is really bad, I just dropp it. Sometimes there is no point in continuing a really bad drama. I have tried, but it just feels bad right after, and you will feel like you have wasted so much of your precious time. 
I force myself to finish it, but if it's something I really can't enjoy, I just drop it.
If it's really horrible to the point where I can't tolerate it anymore, I'll drop it. But usually, I like to finish them because I hate not knowing what happens. D:
I have droped a few but allways try to finish,but if it does not pull me in after 2 or 3 episodes i just feel there is no hope.
I don't really like to drop drama's, since I wasted hours on it..
Sometimes I use the skip method, just skip the boring parts you know, currently trying to do that with DOTS.

And most of the time the end is better than the beginning, so I finished Goblin even though the beginning was a bit meh for me.
After suffering through The Heirs, I realized that I need to drop unworthy dramas, though sometimes I don't realize they are unworthy until the last ep ^^;
But I do start any drama without prejudice and give it a couple of eps before deciding...
Sometimes I do, most of the time I don't.

Half the time I skip to the last 2 episodes if I get really fed up and see how it is lol
I usually drop dramas that I don't like after around 3-5 episodes. That's why I my Completed dramas are usually rated pretty high because I liked it enough to stick with it.

Once in awhile I force myself to watch more because it got rave reviews and I want to see what people are talking about.

Actually taking part in the Watch Challenge sometimes makes me try to finish things that I'm not that into just so I can put it on the list.
Woah .. u atleast take it to the 6th episode... i actually stop in the middle of the 2nd episode if i start hating the first episode
but i sometimes force myself to the end .. because i have this little bit of 1% grantee that it will be great in the next episode..
but at the end of the drama it will be a utter waste and i will start regretting but at the very end at some point i will be glad i watched it ...:"D
Most of the time if I reach the 7th episode, I do end up finishing it. But, if i've only watched 1 or 2 episodes and I find it to be a drag already then I drop it right away. Other times I drop dramas that I'm so close to finishing just because I find them impossible to continue. I hate doing that though, so I try to watch dramas I know i'd end up enjoying.
I tend to stick it out for a few episodes but if I'm really not feeling it, then I'll drop as I don't feel like investing that much time into something I'm not enjoying, especially if the drama is long.
I tend to do the same with neo. after I find myself not enjoying the drama anymore, I'd still give it a few more episodes to redeem itself. but if the cringing is out of control. I usually just dropped it.