I wholeheartedly second Korean Drama "My Girl". I cant think of a drama better then that one. I love it!!! Its funny, heartwarming, and everything thats NOT a Korean drama. Its so different from the other ones. And Lee Dong Wook is to die for...
So hot XD
Japanese ones, GTO is kickass. I'm a big fan of Takashi Sorimachi.
, There's also Orange days. Its another big one that alot of Japanese people like.
Attention Please is good.
Also liked Busu no Hitomi Koishiteru (something like falling in love with an ugly girl. something like that) - I watched it in Japan and liked it. Its pretty funny although at times can be odd.
If youre looking at something a bit more historical,
Hwang Jin yi (Korean) about a Courtesan in the Joseon Dynasty. (Base on the real hwang Jin yi)
Ooku Dai- ishou (Japanese) - Its about the inner palace of the Tokugawa Shogun. The inner palace is where the wives and concubines live. I watched this in Japan and I loved it! I cant seem to find it any where though. Its like 6 years old.
All the stuff I wrote about is a few years old but oh so good!
The last 2 and My Girl are my fav though