1st J-Drama (and 1st drama, period): Hana Yori Dango
1st K-Drama: You're Beautiful
1st T-Drama: Er, started Easy Fortune Happy Life and dropped it and haven't gotten around to trying any others...
Like many others, I started with anime and manga and like the person a bit above me, it was Hana Yori Dango that led me into dramas. Life soon got swamped around then and I dropped anime/manga/drama/thewholeshebang, but recently I've been getting back into dramas, particularly Korean ones. I probably won't get back to anime...I seem to have lost my taste for it somewhere along the way XD