Some I've watched and liked were already mentioned.
Recently I've watched a short japanese drama, and I was amused by the quality of it! The first episode could easily be a short movie, so well done, I was really surprised.
The name is: Kuzu No Honkai
Although, because the drama is meant to be very instrospective, it's not really for everyone, but I do enjoyed the story too, since I like things with more depth, :)
It's short, 12 episodes of 25 minutes each, I would recommend you to give it a try, the direction was really good.