Ugly Alert 133 episode, I do skip few parts but the drama is worth watching.
Smile, Dong Hae 159 episodes (didn't watch the whole thing, just knew the start, middle and end)

Queen Seon Deok 62 episodes (longest drama I've watched from start to finish)
Queen Seonduk (62 episodes)
Currently watching Emperor Wang Gun with 200 episodes TT___TT
Dong Yi (60 episodes). 
@mei-255 just finished this one too
High Kick! The revenge of the short Legged 123 Episodes
Emperor Wang Gun (200 episodes)
boys over flowers! I generally watch dramas which has 20 episodes. But it had 24/25 episodes. Which is the longest till now!
Pink Lipstick. 
It has 149 eps. I've seen well over 100+ eps of it (I don't remember exactly as it was back in the day....) and have not come back to it because I don't know where I am. Even though I know I am so near the end after all these eps...

EDIT: Actually I did not realize it was longer, but Unstoppable High Kick has 167 eps, and I saw alll of it! So that would it :D
Ugly Alert!! Still my favorite drama 

Close second is My Daughter the Flower (131 eps) not worth
King's daughter Soo Baek Hyang 108 ep
Queen Seon Deok for me (62 eps) and what a ride! One of the best historical drama I watched.

One Well-Raised Daughter Ha Na
122 episodes total but I'm on ep.60 :)