My list is small compared to a lot of user on here since I'm more of an Anime fan than an Asian drama fan but I do enjoy watching drama. Also, I started watching both Japanese/ Korean drama around the late 1990s since my family watched Japanese drama on TV daily. Both my father and my mother's family side was a big fan of Abarenbo Shogun when I was younger. 

The sad truth about watching Asian drama in the 90s, you either had to watch it directly on TV or set it on time record onto a video tape, or the last resort is to go to a rental shops to rent videos without English subtitles or buy fansub tapes off on Ebay.....Lastly, if you are lucky enough, find someone who recorded the drama and then you could borrow those tapes from them.....so there weren't many opportunities to watch dramas back in those days so I'm grateful for nowaday's modern technology and streaming websites, as I can watch dramas anytime and anywhere.

My favorite 90s Japanese dramas are Kamisama Moukoshi Dake and Koori no Sekai.