I feel the same way about Disney Channel, I wouldn't even watch it as a 10 year old because the shows were so unrealistic and just plain bad. With that said, my favorite shows are The Office (Netflix has it, and it is on TV but I don't like the ninth season), Modern Family (available on Hulu or every Wednesday at 9/8 central on abc), Futurama (on Netflix), The Walking Dead (also Netflix), and House M.D. (Which I couldn't find on Netflix OR Hulu, but I'm pretty sure it's on Cloo). Hope this helps! :)
Pokemon, One Piece, Death Note, Kuroshitsuji, Soul Eater, Hetalia, Elfen Lied, Highschool of the Dead, Deadman Wonderland, Doctor Who, Tales From the Darkside, American Horror Story.
Those are the shows I watched when I was 13, I'm still just 14 now, so there's not much of a difference. Most of them are anime, so you may or may not like them. As a general warning; Elfen Lied and Highschool of the Dead contain a lot of nudity and sexual scenes, Deadman Wonderland, Highschool of the Dead, and Elfen Lied have a lot of gore as well, and most of them have strong language, so you may want to know what you're getting into ahead of time before you start watching some of the shows (with the exception of Pokemon and Doctor Who). The only really "mature" ones are Elfen Lied, Highschool of the Dead, and American Horror Story though.