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Mine was Goong! But my whole run really began with Boys Over Flowers
I have watched some historical Kdramas before but 'the heirs' was the drama that made me really addicted.
It was Goong for me. My first kdrama. :-)
boys over flowers, lol. My first kdrama was You're Beautiful which I watched after completing Ikemen Desu Ne though
My first K-Drama was Coffee Prince, but I didn't think I liked K-Dramas at the time. I think it was Vampire Prosecutor and Faith that really won me over. Now, of course, I know how awesome Coffee Prince is haha! But I think I watched VP because it was on Netflix and I could watch it on my TV at the time (if feels so long ago). 
My gateway Korean drama was Coffee Prince, I had seen a youtube video of Eat Your Kimchi do a tour at the filming locations and going crazy about it. It came up on Netflix so I thought I had to try it. 

Though, I only really became addicted with my next Korean drama, Boys over Flowers lol. 
My gateway drama was secret garden, which was also my first K drama (although I had watched lots of mandarin movies and Japanese variety shows)...
Mine was Dream high. No Regretsss. Since i watched this drama i start addicted to korean dramaa yeepp.
First was That Winter The Wind Blows, became addicted after Innocent Man.
For me it was You're beautiful, I started it because it was the number one drama on dramacrazy. I didn't really like that drama but I ended up looking for other dramas and it was game over. the first korean drama that got me hooked was Baker king, kim tak goo. 
i watched some dramas on tv but i never got really interested untill i watched the heirs it was the sparkle that lead to the magical dramas i watched till now
The first k drama i saw was my girlfriend is a gumiho..after that i cant get enough of them and i have watched that like 5 times
So, I'm actually pretty new to kdramas, I probably started watching in April of this year. 

The first drama was Fated to Love you (Korean version), but I didn't finish it until after I watched My Love From Another Star & Master's Sun. Those two really, really cemented my kdrama fan-card. 
the heirs and I haven't been able to watch either a Lee Min Ho or Park Shin Hye drama since...nothing beats their chemistry