It has some violence, but it's realistic and reasonably paced out, similar to The Wire (going by memory I might say that The Shield had just a little more violence, but I wouldn't swear to that). It's a finished story, I believe there are six seasons of 10-15 episodes each. It's about a police precinct in Los Angeles, and focuses on a foursome of officers who have been tempted down the road of breaking the rules for the sake of doing their jobs better, but then go too far, and the further they go the less chance they have of turning back. There's an interconnected side story about two detectives in the precinct that runs all six seasons as well, and is usually very interesting. It's a compelling series.

I would personally rank The Wire a little higher than The Shield, if only for the depth of their social commentary, but The Shield is very good as well.

My second recommendation is a series that is not quite finished yet ... but it only has one season left, and I believe it will start to air this summer, so it'll be fair game very soon. That would be Breaking Bad. It's about a chemistry teacher who gets cancer and decides to turn to meth production in order to leave enough money for his wife and children when he goes, since he has nothing to lose. But as the series goes on and he gets deeper and deeper in, it turns out he has an awful lot to lose after all. The main actor has won an Emmy for best actor pretty much every season the show has been on, if that tells you anything. It's a fantastic show, and my favourite thing that's currently on air. There are four seasons finished so far, with the fifth and final airing soon.