I want to watch a good TV series on Netflix. I am looking for something that meets these criteria.
Sci Fi:
Firefly
Original Star Trek
Farscape
Mystery:
Longmire
Columbo
Luther
Sherlock
Life
Lie To Me
Flashpoint
Magnum PI
Miami Vice
Longmire has been picked up for a fourth season to air on Netflix
Yes, it has
I suppose Sherlock and Luther both have a potential another season as well
If you like mystery and history, Foyle’s War is pretty good.
Just checked; last episode was Jan. of this year according to Wikipedia.
Fringe
Not sure it’s considered a mystery, but I quite liked Leverage.
Broadchurch
Netflix has Season 1 and there are more, but the season stands on its own as the beginning and end of a single case.
Terriers is an interesting series in the mystery realm. It’s complete, although there has been talk about another season. I wouldn’t say it ends great, it seems to have a hasty wrap-up because of it’s impending cancellation, but It stars Donal Logue, and some guy named Michael Raymond-James in the part that should have gone to Kevin Corrigan. But it is just 13 episodes, not too much investment if you don’t like the ending.
ETA: Sorry, I only see this on Amazon.
I would add Midsomer Murders and possible Inspector Morse to the list of mysteries. These are both British series and well worth the time to watch. Both are 90 minutes per episode, also. I much prefer the British cop shows to American ones, but I am not sure why.
Bob
We’re currently loving “Ripper Street.”
I don’t know how it ends.
Luther isn’t exactly complete. There’s a prequel short series/movie coming in the fall.
But watch it anyway.
Psych. Guy pretends to be a psychic, solving crimes for the Santa Barbara PD. Great show, mystery/comedy, and the chemistry in the cast is fantastic.
Eerily similar to The Mentalist, or so I hear.
There ability to self parody was pretty good 
I enjoyed Jericho. It’s about a small town in Kansas after a nuclear war. With Skeet Ulrich.
You should watch Daredevil. It is extremely well done. It tells a season long story but does leave some plot threads because it is an on going series (which has been renewed so no worries about being left hanging).
This will be divisive but I would recommend Lost. The ending was disappointing for some (many?) but at the time I found it satisfying and the journey you take there is worthwhile.
Death in Paradise is an old-fashioned murder mystery of the British cozy variety. The detective finds the clues then puts all the suspects in a room to explain who the murderer is.*
The show is ongoing, but there is no story arc, so there’s nothing that carries over. Season three was just put up.
The Miss Fisher Mysteries are the same. There was a story arc in the first season, but they’ve gone back to individual episodes.
The entire series of Misfits is available for free on Hulu if you don’t mind watching it on your computer. While it is only very good toward the end, the first two seasons are excellent.
*They wink at this trope in the third season.
IIRC, there’s a mini-arc concerning Jack and Deputy Commissioner Sanderson toward the end of the second season.
This is the one I thought of first. Excellent show, and damnable to have been killed off after one season. It’s worth the time as long as you don’t get too caught up in it and thus join the ranks of people (like me) who bitch at the idiots who cancelled it!
To whet your appetite, check out Terriers TV series Episode 1 Pilot