You're Beautiful. I loved it a lot, and it made me interested in K-pop as well.
Still It's the only one I watched so far, but I already downloaded many other K-Dramas.
Mine was "Full house" (2004)
'Stars falling from the sky' was mine. I came across it on Netflix and was like 'well....this is really weird', but then I couldn't stop watching it
Playful Kiss. I loved it at the time because I loved the anime, but... you know. Not the greatest acting and yeaaaah
Iris..  I watched it like an year or something? ago and I was just getting into kpop and I was totally obsessed with T.O.P and It was dubbed in my language so I decided to give it a try and later I regretted it thousands of times  bc It spread like ebola and I couldn't stop watching dramas and holy jesus  I still can't т.т
BOF and Personal Taste
I accidentally found on youtube movie Always with So Ji Sub and after I madly fell for him I searched more movies with him but I found What happened in Bali drama.So, my first drama was What happened in Bali. I watched it twice in a row. :P
Boys before flowers followed straight with Playful kiss...I can say that Playful Kiss was bigger push then BBF <3
You're Beautiful. I watched the last 6 episodes first since my sister was watching it. XD I cried after it ended, I was just in love. lol
The first kdrama I came across was BOF. Didn't finish it, never will. Playful Kiss was my gateway drama but Secret Garden and Coffee Prince made me stay.
Mine was You are Beautiful. Not only to Korean but dramas in general.