@Ricky  LOLOL That second lead! XD. Queen In Hyun's Man is one of my all time favs, and the first one I thought of, so definitely check it out. Other ones....

Angel Eyes- He really isn't much of a competition and since theirs a childhood back story you really can't love anyone else
Autumn's Concerto- One of my favs, no second lead :)
City Hunter- (WHY IS THIS NOT ON YOUR LIST?!?!?! It's a classic go watch now!)
I Hear Your Voice- The second lead is not worth anything. One of my all time favs!
Innocent Man- Revenge drama so you'll hate the second lead (with immense passion), but the story is great!
You who came from the stars- The second lead is written off by the main character, so you can write him off as well!

Although it's an old post. I would like to add one.
Strong Woman Bong Soon- ML was too sweet to handle. Also the SL did not create any hindrance. Even in the first few episodes The ML had a funny crush on SL :vvv Do watch this... Their chemistry was top notch...

Piece of your mind- Really, I think the only one out of very few dramas in the kdramaland which makes you feel what true love is even when you didn't experience it before. Don't know why it's so underrated, don't know why people always miss to mention it.