I'm not a huge fan of Korean dramas. I think they're way melodramatic. Someone is always dying or having amnesia and other soap opera shenanigans. But my whole family is into them. Whenever my brother breaks up with a girlfriend, all he does for about 2 weeks is watch Korean dramas non-stop. I think it's like therapy to him. I'm attempting to watch more Korean dramas to improve my Korean though.

I got recommendations to watch:

Full House
Boys Before Flowers

South Korean films on the other hand keep getting better and better imho. They've had a real revitalization in their film industry. Still a huge taste for the melodramatic though. A hugely popular film a year or so ago was A Millionaire's First Love. If you cried watching Windstruck, you'll probably cry watching this too.