Currently? Just Cosmos for myself, though I have to admit that Peg+Cat and Word Girl are fantastically well done for kids' shows, well enough that I find myself actually looking forward to watching them.
Just shows currently on:
How I Met Your Mother (technically correct is the best kind of correct)
South Park
Brooklyn Nine-Nine
American Dad (though I'm really behind on it)
Currently:
How I Met Your Mother, Big Bang Theory, Castle, Community, Walking Dead (though unless the finale teases anything promising, I think I'm dropping the show), Luther (not sure if there'll be a fourth season), and of course, Doctor Who
Previous or ended: All DC Animated Universe (Batman, Superman, Justice League, Batman Beyond), Young Justice, Spectacular Spider-Man, Boy Meets World, Scrubs, Firefly, Buffy, Angel, Dollhouse
S.H.I.E.L.D.
Brooklyn nine nine
Justified
Modern Family
The Americans
Community
Parks & Recreation
Grey's Anatomy
Scandal
Hannibal
Girls
Mad Men, The Bridge, True Blood, Game of Thrones, Louie, The Newsroom, True Detective, New Girl, Person of Interest, It's Always Sunny, The League, Review, Key & Peele, Drunk History, Archer, Comedy Bang Bang, Portlandia, House of Cards, Orange is the New Black, Cosmos
geez, and I think that's only stuff currently airing / airing soon
SHIELD
Big Bang Theory
How I Met Your Mother (just came back for the last season, stopped about 2 years back)
Ultimate Spider-Man
Avengers Assemble
Top Gear
Amazing Race
Dallas Stars Hockey
Doctor Who, Survivor, and The Blacklist. I don't spend much time watching tv, maybe because I spend too much time installing it. Most of my "me time" is on Minecraft or playing guitar.
I do love The Blacklist though, it answers fewer questions than it raises.
Community
Archer
Parks & Rec
Doctor Who
Orphan Black
How I Met Your Mother
Mad Men
True Blood
Gravity Falls
Adventure Time
I say voluntarily because there are a few shows I've seen most of their episodes because Mr. Z or Li'l Z like them. For example, I am very up-to-date on my Sesame Street viewing, and probably a good chunk of the Nick Jr./Sprout/Disney Jr. programing. I also think I have every episode of Ni Hao Kai-Lan memorized at this point.
Currently airing? Pretty much just Grimm, Community and Archer.
When they start back up again, I'll probably be watching Venture Bros, Game of Thrones and Gravity Falls.
The list of things I like to watch that are over would be way too long to list, but the favorites I keep going back to are Babylon 5, Ghost in the Shell:SAC, Firefly, Big O, and, oh, 10 or 20 others.
I also have Hornblower and Sharpe on DVD. No regular TV for me since 1993, my gf has hers running all the time and I hear a lot of it from theroom next door; german TV of course, mostly everything Star trek lately. Though some of the new series sound funny I don't have the time, or more precisely don't want to put that time into TV again as I did before my abstinence time. I was almost addicted to the screen. These days my time waster of choice is MMOs, I'm a serial monogamist there.
Of coure I have GoT on DVD, getting season 3 just next week, hah!
Currently watching Blacklist, Almost Human, Cosmos, SHIELD, Archer and various anime. When the new seasons start I'll be adding Sleepy Hollow and Doctor Who back to the list.
Finished shows would be Scrubs, Harvey Birdman: Attorney At Law, Space Ghost Coast to Coast, Metalocalypse (far as I know Doomstar was the ending, could be wrong), Monty Python, Firefly, Buffy, Angel, and again, various anime.