Many of the popular ones don't have any heavily rated content...
but at any rate, the more recently popular dramas, as listed above are:
Hana Kimi (Japanese) | Meteor Shower (Taiwanese)
Hana Yori Dango I and II
Zettai Kareshi (eng: Absolute Boyfriend)
Gokusen 3 (which I think is a bad show and overrated)
and a good one that's still being translated that I think might become popular is Osen.