Nobuta wo Produce - a heart-warming, touching drama
Seigi no Mikata - comedy (with sides of romance) and a female lead that had me laughing through out the drama
The Queen's Classroom - there's a Korean version, but I haven't watched that one. The J-Drama is really, really good though, with memorable, lovable characters and a well-written, well-acted script. It's the sort of under-rated gem that usually falls under the radar (because it doesn't have romance and because its premise is a bit overdone). I think I find this so memorable because the female lead is so unapologetically tough (and a bit intimidating and mean sometimes), she reminds me a lot of Professor Snape really, and that sort of personality is really rare to see for female characters in fiction.
Gokusen is another badass female teacher, although this verges more on comedy and action than the former. It's a bit unrealistic, but it's really charming and entertaining watch nevertheless.
Biblia Koshodou no Jiken techou - is a j-drama set in a bookshop and is about a shy, introverted girl who unravels mysteries. This one is charming and cute and kind of calming, relaxing watch. I haven't finished with it yet, but I'm really love it so far.
