Most of these 5 are finished series, so you won't have to wait for a next season to come.
I know, the name sucks. It's not very appealing but at the same time, if you love detective shows, you'll love this. This series is an American version of a Danish one and was originally done by another network (can't remember now) and cancelled after season 2. Fans complained and Netflix listened and they picked it up for two more seasons. I gotta say, after it was over I missed the two main detectives so much! They're so real and relateable and I just loved them. The first two season focus on one murder and every one involved has something to say and an interesting back story. Season 3 and 4 are two separate homicides but still extremely gripping.
This is another Netflix original set in Ireland. Starring the guy from 50 shades of gray and the woman from The X Files (I am so good at research), it's a detective drama that sucks you in immediately. Only two seasons but excellent!
I loooove this show! Some people say that it should have ended on season 4 but I was happy it continued. This is the story of Amanda Clark that resurfaces from anonymity to avenge the wrongful conviction and dead of her father. Because I am a justice maker and I wish I could take justice into my own hands, it was very interesting to watch someone else do it, even if it was a fictional character. But all of those involved in this drama are extremely deep and interesting (I know I say that a lot) and each one has an agenda, Amanda has to make sure hers prevails. All seasons on Netflix.
The Walking Dead (not finished, only 5 seasons on Netflix, season 6 is currently airing)
By the time you're done with season 5, season 6 will probably be available to stream. I wasn't into this show, in theory, I had never watched it but I knew zombies weren't my thing. But people kept on insisting so me and my hubby gave it a chance and we-were-hooked! I think one of the main things that makes you follow it up even though it's true, sometimes it seems like it's a neverending series of unfortunate events, are the characters, even more so than Lost. In The Walking Dead you grow close to each of the characters and you keep watching the show to know what happened to them, but I still think is super entertaining.
Criminal Minds (9 seasons on Netflix, 10 currently airing)
Here you have pleeeenty of episodes to get entertained. Another detective tv show, this one is more focused on the cases, from the perspective of Behavioral Analysis agents from the FBI that study criminal minds, like the title says. I do wish there was a bit more of character development though because each of the agents is amazing.
I hope you follow my advice and check these shows out! Of course there are other ones I could recommend as well, and maybe I'll do a part two. But these ones I feel are the must watch ones. What are your must watch shows? Let me know!