@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!