I just finished a Korean drama this past Saturday. It was called Glass Slipper (I think). I only watched the last two episodes though, but I understood the whole story for the most part because my auntie explained who the characters were and their relationships. It was a really sad story, and I can tell why she's (and other people) are addicted.
I have My Sassy Girl on DVD and that movie is hilarious, and a little romantic. I've also seen My Sassy Girl 2 (I only know the Japanese title: "I Want to Introduce My Girlfriend"), but the first is still better IMO. I know that it's not officially My Sassy Girl 2, but that's how I first heard about it so I call it that.
I usually don't watch much drama, except for a little Japanese drama every now and then, because I can never seem to catch one that's just starting. My gf, on the other hand, loves anykind drama: J, K, and HK drama for example, so now I'm more open to watching whatevers.