Oh, I definitely second the recommendation for Dae Jang Geum. Gosh, that show is so fantastic; I can't sing its praises enough.
Also, any Detective Conan fans might want to try out Damo. I will admit, I prefer the earlier episodes because they're more Conan-y than the later ones, which have more of an ongoing plot and, IMHO, a bit too much wire-fu for my liking. But I still enjoy the entire series.
And the Meteor Rain listed here seems to be a Meteor Rain special. At least, I think the series is supposed to be more than 4 episodes. Still, it seems like a nice special, and I did enjoy what I saw of the series.