A lot of great series have already been named. I would add the following:
- Cruel City (Nice plot, action packed, bit of romance too)
- Sungkyunkwan Scandal (Historical, gender-bender, romance, humor, nice character build-ups, intelligent female (!) and good story)
- Queen In-Hyun's Man (Time-travel, wonderful couple, sweet and solid)
- Shut Up: Flower Boyband (Friendship, romance & bromance, not a complicated story but it does make you think about life and especially friendship)
- Vampire Prosecutor (Not like Twilight (no shiny nice romantic vampires), action and mystery, a (very) small hint of romance)