My wife and I have enjoyed the following shows on Netflix:
Retribution: Excellent single season mini-series. 4 one hour episodes only, but they are pretty riveting. Follows two families whose children were recently murdered. Great drama and suspense. Highly recommended, even if it is a little short.
Alias Grace: 6 part limited series. Really interesting 19th century period crime drama about a young woman accused of murder. The main actress is also gorgeous, so that definitely helps. Highly recommended
The Keepers: Real life crime documentary about the murder of a nun and links to corruption in the Catholic church. Very interesting and highly recommended.
The Magicians: Kind of an R Rated/Mature Harry Potter Narnia magic show. New episodes are still airing on SyFy, but you can get caught up on the first two seasons with Netflix. A lot of fun, but nothing too serious.
Containment: Decent drama about an outbreak and quarantine situation. A little cheesy at times but still enjoyable. 1 season
Crossing Lines: International crime series. Kind of like Criminal Minds, but a team of agents from different countries. It was pretty good for 2 seasons, and then they almost completely changed cast for season 3, which made it hard to finish. If you are looking for some fun crime drama, it's worth it for the first two seasons at least.
Breakout Kings: Short lived but fun series about convicts put on a team to catch escaped convicts. The characters are all pretty good, especially Jimmi Simpson's character. Only 2 full seasons though.