If I remember correctly it was You're Beautiful :D
The first Korean drama I watched that got me hooked was Full House. Such a weird drama, but I had never seen anything like it before and could not stop watching it... than I went onto A Love to Kill, Big, Secret Garden, Dream High... and I was hooked.
My first every drama was Mars, but I only watched it cause I read the manga...the drama that I consider my gateway into dramaland was the second one I ever watched called 'Stars falling from the sky'
Although the first ever is Boys over Flowers, I wouldn't recommend it to kdrama first timers.
Boys Over Flowers and I loved it then... but now like the Comment above me said I wouldn't recommend it to first timers either 
I think that for me it was You're Beautiful 
MIne is Princess Hours. That was like... 8 years ago? Since then, I became a Koreanophile. :)
My first korean drama was City Hunter -- about a month or two before the same friend that had introduced me to j-dramas with Hana Yori Dango, introduced me to k-dramas with City Hunter. Up to then I stubbornly refused to watch anything that wasn't japanese and Hana Yori Dango style (as in light, romantic and funny), but City Hunter was so different it truly hooked me... Now I like both styles, although I do prefer heavier, deeper dramas ever since :)
Boys Over Flowers, it was my first Asian drama.
But I think the Japanese version is better ^-^
The first drama I EVER watched was Sunao ni Narenakute. My roomates in college watched because they loved KPOP & DBSK's Kim Jae Joong, but the 1st drama that got me hooked was Biscuit Teacher Star Candy with Gong Yoo & Gong Hyo Jin
The first Korean drama that I ever watched was Sweet 18 with Lee Dong Gun and Han Hye Jin, which I watched together with my Korean American friend. 
It was fluffy and funny and different and sparked an interest about other Korean dramas!

:)
Mine was Succesfull Story of a Bright Girl. That was the first k-drama I ever watched in my life. And I loved it. :)