So here goes:
Hana Yori Dango
Boys Before Flowers
Witch Yoo Hee
Atashinchi No Danshi
Kimi Wa Petto
Mei-chan No Shitsuji
1st Shop of Coffee Prince
Stars Falling from the Sky
Devil Beside You
And I'm probably forgetting some, but that's just about it.
I'm currently halfway through Secret Garden (below).
Yes, I admit that dramas may be shallow or "cheap". But they are a satisfying escape into a completely different world from the one I live in. I watch them not find some deep form of enlightenment, but enjoy them and the characters in them.
So if you're bored and looking for something to do, I would suggest trying one out. My favs are probably Full House and Hana Yori Dango and Secret Garden. Watch them here (hulu) or here (this one has rankings and such.)
Oh and if you DO watch one- make sure you watch as least the first two episodes before deciding whether or not you like them as with anything the first episode is the most boring, comfusing, and weird of all of them.