pretty much any of the shows by either J.J. Abrams or Joss Whedon. i can't really think of an exception unless you want to count a show just being dated.
top choices from both would be Lost & Firefly.

Dexter
Breacking Bad
American Horror Story
The Mentalist
True detective

I strongly recommend Firefly. Be sure to watch the episodes in order

"EASTBOUND AND DOWN" YOU WILL LIKE THIS!

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I'm not sure when you say "the show must have ended" means the season ended or the entire show.

I have only watch 2 new shows and I enjoyed them a lot. Each season has ended, but both shows will be returning with new seasons. They were Bates Motel and Stranger Things.

All my other favorite shows are much older and have ended: X-Files, King Of The Hill, Malcolm In The Middle, Home Improvement, Roseanne, Seinfeld.

Daria
Galavant
Black Mirror
LOST

breaking bad

Like everyone else has said Breaking Bad is a must.
One I haven't seen anyone mention is Hannibal. It's dark and can be pretty gruesome but if you don't mind that it's SO good. I rewatched the show with my brother a month after binging it and still loved it just as much the second time around.

Stargate:Atlantis, Childhood's End, HBO's Carnivale, Utopia

Battlestar galactica (2004), Sons of Anarchy, Rome, Breaking bad, Spartacus: Blood and Sand, Stargate Atlantis and SG1 if you like spacey adventure stuff...

I don't know if anyone's mentioned Fargo yet. It's still ongoing but each season is a separate story so it kinda counts. Also, Hannibal. And if you're into anime check out Samurai Champloo

How to Get Away With Murder season 1 was amazing! Haven't had time to watch season 2, but I'd definitely recommend giving it a watch.

House.

Stranger Things
Twin Peaks

Cosmos: A Spacetime Odyssey
Breaking Bad
The Wire
Carnivale
One Punch Man
Stargate

Watch "The Shield"
7 (?) seasons
http://www.imdb.com/title/tt0286486/?ref_=tttr_tr_tt
It's every bit as good as you hope. And it has one fo the best endings of any multi-season show. I love it. Love it. Love it.

The first season of War of the Worlds. And ONLY the first season. Season 2 is best ignored. War of the Worlds was basically X-files before X-files, and it's quite good.

Gilmore girls!

Black Mirror is pretty good, different story every episode so although it's not over you don't really have to wait for more episodes.

Psych. <3

Danger 5, you gonna love it

Don't watch much tv anymore, but have a fondness for sci-fi and fantasy. Battlestar Galactica, Babylon 5. Like Supernatural but not sure if that is still running so... Also liked Being Human, but only saw 2 seasons before they yanked it off. Watched the US tv series but they also made a British series.
And thanks for the gibs :)

I'm going to go with some of my favorite old school shows...

Mission: Impossible (Yes, this is the TV show that the movies are based on, but I much prefer the TV show)
Kung Fu (Watch Kwai Chang Caine kick ass in the old west)
The Twilight Zone (No need to explain this one. If you are allergic to black & white shows, stop whining and watch it anyway)
Star Trek (The original series, and still my favorite of the bunch)
M*A*S*H (It's funny but also serious, early seasons are more comedic and less serious than later seasons)
Taxi (One of my favorite sitcoms)

The Wire.