Mine was To The Beautiful You, I love SHINee now, and you can guess whose my favorite haha... He needs to be in more dramas!
Dae Gang Geum aka Jewel in the Palace - after this one there was no looking back!  Started with mainly historical dramas like Dong Yi and Yi San then began watching more modern gems.
Sad love story ... this drama i will never forget 
Oh! My Lady was my first. 
First I have Netflix to thanks and then Lie To Me.
It was started from Personal Taste
Mine was "Personal Taste" ~
From what I remember, my very first korean drama was... Full House ! I think I watched japanese dramas before but I don't remember the first one. Probably a manga adaptation.
Full House (the original)
My first one was "Lie to me", but the one that really turned my life around was "49 days".
Mine was 'Full House' <3 Rain <3 (goodness I was 14 when I started watching these magical dramas) 
BOF and Coffee Prince...
My first drama in the fall of 2012 was Padam Padam and while I liked it I don't consider it my gateway drama. My gateway drama was Lovers. I watched it late spring 2013 at a time when I was about ready to abandon Asian dramas for good. But I ended up loving this drama so much that I decided to stay and I'm still here today.