I've had the Starz streaming app for the past few months, and there are a number of good series on it.
Some of my favorites are:
"The Missing": A detective searching for abducted children. Season 1 was inspired by the Madeline McCann abduction case, but I think season 2 was the better of the two seasons.
"Boss": Kelsey Grammer plays the mentally deteriorating Mayor of Chicago trying to keep his grip on power, and his sanity!
"Luther": Idris Elba as a rule-bending London detective....I'm only through Season 2 of this, but its one of the better cop dramas I have seen in a while(its 10 years old, so I assume many people have already seen this one!).
On Netflix, I just wrapped up a show called "Imposters" which I thought was really good. Apparently, this show was originally on Bravo.....I thought that channel only made Real Housewives and crap like that...I bet this show would have gotten more praise or attention if it was on a regular channel, definitely worth a try. Its about a group of scammers who marry people, steal everything their mark has, then disappear without a trace. The show revolves around three "marks" who band together to find the woman who scammed them(of course they are all still into her). The lead actress who is the scammer is a real beauty....never seen her in anything else before, but man she was a perfect pick for the part!