I started many years ago with movies, essay ones by Chinese or Japanese directors. I simply loved their setting, the costumes, the stories told. I lived in south-east Asia for a while myself and the addiction to everything asian has always been there, although I didn't even know of their dramas.
One day I ran out of good Chinese movies and decided to watch something online, coming across The Returner with Takeshi Kaneshiro, then I can't remember how I stumbled upon Tada Kimi Wo Aishteru and decided I needed more of Hiroshi Tamaki. Through a couple of other movies I finally landed on my first J-drama: Nodame Cantabile. I was hooked. From there on it became a sort of frenzy, out of which I also had the grand ambition to learn Japanese - an ambition I haven't given up on yet. Good plan, Rita. Now I can go to Japan and declare my love to the first taxi-driver I come across in his native language... :P
My first K-drama was... hmm... My Girl, I think. I liked it very much, and went on with Boys Before Flowers. Finally I watched Coffee Prince and that was the drama which really made it for my Korean-drama addiction. For the love of symmetry, now I can go to Korea and declare my love to any chapchae noodles express deliverer in Korean.
My first Taiwanese was Autumn's Concerto and I'm glad it was so, for I still consider it one of the best Taiwanese dramas out there. Had I tried with Devil Beside Me or It started with a Kiss I would probably have given up on them.
I can say "wo ai ni = I love you", in Mandarin, by the way... ;)