I really liked the cop series "The Shield" (some violence, but not tons), and haven't watched The Wire yet. Breaking Bad is a TERRIFIC drama and story is excellent - you'll laugh, you'll get a tear in your eye. There is some violence at times, but it's all about the tale, and I recommened it, too. :D
Another really good drama I've been watching is Nurse Jackie.
haha, I'm recently housebound and was never a TV watcher, so now I try to find good ones. The prison drama OZ was one of my fav shows ever, too (HBO).
:)