Most of the Asian dramas I've seen are Indian serials, and I'm not sure if they'd count. My family is TOTALLY into them. Needless to say, many of them are redundant. Most of them star a middle-class young female, normally not all that educated. She strikes it lucky by meeting the son of a rich businessman, and said son will either dote on her or hate her guts. In the former, her in-laws (well, mostly mother-in-law) will hate her and make ever attempt to burn her to crisp (like Marie Biscuits :D). The latter, the SON will want to make kulfi out of her. There will ALWAYS be a female antagonist, who can be the cookie-loving mother-in-law, the vain sister-in-law, the sister who wants some hubby love, and/or the estranged lover of the husband who hates her. Either way, she will wear shitloads of mismatched makeup with fanservice (cleavage, sleeveless sari blouse, etc.) and have tons of screentime talking in her head and displaying the camera crew's video effects skittlez.
This parody is ironically very accurate.
This one, while not in English, is pretty much Indian soaps in a nutshell (shout-outs at the beginning for Marathi telesoaps!).
Other notable points include DORAMA in the kitchen (like ten episodes on who the hell will make rice pudding and cut the vegetables ONOEZ), tea time dilemmas (vamp switches sugar with salt, making tea a salt-fest), and the flood of tears Miss Heroine will shed because she's a goddamned doormat. Now, there are some good shows. My favorites on the desi side include, Jhansi ki Rani, Baa Bau Aur Baby, Khichdi, Sarabhai vs Sarabhai, Tarak Mehta, and Astitva.
I never got much into Japanese dramas - the main two I've seen are Pretty Guardian Sailormoon and Summer Snow. I saw a little bit of Winter Sonata, but that's because a good friend of mine is into Korean dramas.