I've really been getting into the Japanese dramas over the past few years too. Well, I've really been into Asian dramas to be more exact. It started with Japanese dramas for me, but it's expanded into Korean and Taiwan dramas as well. I haven't explored many of the Asian movies, but I've also recently started enjoying those
Hmmm... as for the Japanese dramas that I liked the best? (And this is in no particular order)
Gokusen is fun... It does get a little (or a lot) repetitive, especially during the later seasons, but I like the teacher and still enjoy watching it.
Hana Yori Dango (Boys Over Flowers)... yes, it does have about a million versions (The manga, the anime, the Taiwanese version Meteor Garden, the Korean Version Boys Before Flowers, I think there was another Taiwanese version that came out recently? I haven't had a chance to watch it yet.) But yea, point is, I enjoyed it - especially early on.
Kimi wa Petto... Momo is cute! I had a hard time keeping interested in the show to the very end, but the beginning was very entertaining to me. Strange concept (a woman takes on a younger man as a pet), but cute story.
Nobuta wo Produce... Another one that I enjoyed. Noticing the Johnny's theme yet? - I'm guessing you know about JE if you've been watching Japanese dramas. Anyway, the story is good, plus the boys are nice to look at
What else? I've watched so many it's hard to keep straight.
Ruri no Shima... such a sweet story, first drama I ever watched, so I hold it close to my heart!
1 Litre of Tears... So sad, I think I cried a litre of tears while watching it.
Summer Snow... Another sad but good one
Bara no Nai Hanaya... Loved the beginning so it makes the list, but started losing interest near the end
Satorare... About a guy whose thoughts can be heard by everyone - so unique of a storyline
RH Plus... Corny, but cute vampire story.
Daisuki!!... Feel good story
Engine... Another feel good kind of story.
Yea, my descriptions really don't tell you much, maybe I'll add some links to the dramawiki pages later. Or you could just search up the ones you don't recognize. I'm sure you've already seen some of these yourself.