I am a HUGE Drama watcher and fan. The KDrama that got me into watching dramas was "Boys Before Flowers." That drama was amazing. Still remember it to this day. I think I've watched that one at least 3 times and I'm still not tired of it. I don't think I'll ever get tired of watching that drama. It remains as a fond memory.

What I Have Watched Already: 

Korean:

Boys Before Flowers

Heartstrings

Dream High (1 and 2)

You're beautiful

Flower Boy Next Door

Playful Kiss

Line Romance (very short and cute drama)

You Who Came from the Stars

Rooftop Prince

Miss Panda and Hedgehog

Taiwanese: 

Romantic Princess

Alice from Wonder City

In Time With You

Pi Li MIT (Mysterious Incredible Terminator)

What I am going to Start Watching:

Master's Sun

Good Doctor

Trot Lovers (when it comes out)

God's Quiz 4

Roommate (could be counted as a drama)

What I am currently watching:

Fall In Love With Me (Taiwanese)

Doctor Stranger (Korean)

Feel free to recommend me any dramas you watch if you want :)